3つのうち1つを消したものとの包含関係
3つのうち1つを消したものとの包含関係
\(P,Q,R\)は命題変数とする。
(1)
\[ P\lor\left(Q\lor R\right)\Leftarrow P\lor Q \]
(2)重要
\[ P\lor\left(Q\land R\right)\Rightarrow P\lor Q \]
(3)
\[ P\lor\left(Q\rightarrow R\right)\Leftarrow P\leftarrow Q \]
(4)
\[ P\lor\left(Q\leftarrow R\right)\Leftarrow P\lor Q \]
(5)
\[ P\lor\left(Q\downarrow R\right)\Rightarrow P\leftarrow Q \]
(6)
\[ P\lor\left(Q\uparrow R\right)\Leftarrow P\leftarrow Q \]
(7)
\[ P\lor\left(Q\nrightarrow R\right)\Rightarrow P\lor Q \]
(8)
\[ P\lor\left(Q\nleftarrow R\right)\Rightarrow P\leftarrow Q \]
(9)重要
\[ P\land\left(Q\lor R\right)\Leftarrow P\land Q \]
(10)
\[ P\land\left(Q\land R\right)\Rightarrow P\land Q \]
(11)
\[ P\land\left(Q\rightarrow R\right)\Leftarrow P\nrightarrow Q \]
(12)
\[ P\land\left(Q\leftarrow R\right)\Leftarrow P\land Q \]
(13)
\[ P\land\left(Q\downarrow R\right)\Rightarrow P\nrightarrow Q \]
(14)
\[ P\land\left(Q\uparrow R\right)\Leftarrow P\nrightarrow Q \]
(15)
\[ P\land\left(Q\nrightarrow R\right)\Rightarrow P\land Q \]
(16)
\[ P\land\left(Q\nleftarrow R\right)\Rightarrow P\nrightarrow Q \]
(17)
\[ P\rightarrow\left(Q\lor R\right)\Leftarrow P\rightarrow Q \]
(18)
\[ P\rightarrow\left(Q\land R\right)\Rightarrow P\rightarrow Q \]
(19)
\[ P\rightarrow\left(Q\rightarrow R\right)\Leftarrow P\uparrow Q \]
(20)
\[ P\rightarrow\left(Q\leftarrow R\right)\Leftarrow P\rightarrow Q \]
(21)
\[ P\rightarrow\left(Q\downarrow R\right)\Rightarrow P\uparrow Q \]
(22)
\[ P\rightarrow\left(Q\uparrow R\right)\Leftarrow P\uparrow Q \]
(23)
\[ P\rightarrow\left(Q\nrightarrow R\right)\Rightarrow P\rightarrow Q \]
(24)
\[ P\rightarrow\left(Q\nleftarrow R\right)\Rightarrow P\uparrow Q \]
(25)
\[ P\leftarrow\left(Q\lor R\right)\Rightarrow P\leftarrow Q \]
(26)
\[ P\leftarrow\left(Q\land R\right)\Leftarrow P\leftarrow Q \]
(27)
\[ P\leftarrow\left(Q\rightarrow R\right)\Rightarrow P\lor Q \]
(28)
\[ P\leftarrow\left(Q\leftarrow R\right)\Rightarrow P\leftarrow Q \]
(29)
\[ P\leftarrow\left(Q\downarrow R\right)\Leftarrow P\lor Q \]
(30)
\[ P\leftarrow\left(Q\uparrow R\right)\Rightarrow P\lor Q \]
(31)
\[ P\leftarrow\left(Q\nrightarrow R\right)\Leftarrow P\leftarrow Q \]
(32)
\[ P\leftarrow\left(Q\nleftarrow R\right)\Leftarrow P\lor Q \]
(33)
\[ P\downarrow\left(Q\lor R\right)\Rightarrow P\downarrow Q \]
(34)
\[ P\downarrow\left(Q\land R\right)\Leftarrow P\downarrow Q \]
(35)
\[ P\downarrow\left(Q\rightarrow R\right)\Rightarrow P\nleftarrow Q \]
(36)
\[ P\downarrow\left(Q\leftarrow R\right)\Rightarrow P\downarrow Q \]
(37)
\[ P\downarrow\left(Q\downarrow R\right)\Leftarrow P\nleftarrow Q \]
(38)
\[ P\downarrow\left(Q\uparrow R\right)\Rightarrow P\nleftarrow Q \]
(39)
\[ P\downarrow\left(Q\nrightarrow R\right)\Leftarrow P\downarrow Q \]
(40)
\[ P\downarrow\left(Q\nleftarrow R\right)\Leftarrow P\nleftarrow Q \]
(41)
\[ P\uparrow\left(Q\lor R\right)\Rightarrow P\uparrow Q \]
(42)
\[ P\uparrow\left(Q\land R\right)\Leftarrow P\uparrow Q \]
(43)
\[ P\uparrow\left(Q\rightarrow R\right)\Rightarrow P\rightarrow Q \]
(44)
\[ P\uparrow\left(Q\leftarrow R\right)\Rightarrow P\uparrow Q \]
(45)
\[ P\uparrow\left(Q\downarrow R\right)\Leftarrow P\rightarrow Q \]
(46)
\[ P\uparrow\left(Q\uparrow R\right)\Rightarrow P\rightarrow Q \]
(47)
\[ P\uparrow\left(Q\nrightarrow R\right)\Leftarrow P\uparrow Q \]
(48)
\[ P\uparrow\left(Q\nleftarrow R\right)\Leftarrow P\rightarrow Q \]
(49)
\[ P\nrightarrow\left(Q\lor R\right)\Rightarrow P\nrightarrow Q \]
(50)
\[ P\nrightarrow\left(Q\land R\right)\Leftarrow P\nrightarrow Q \]
(51)
\[ P\nrightarrow\left(Q\rightarrow R\right)\Rightarrow P\land Q \]
(52)
\[ P\nrightarrow\left(Q\leftarrow R\right)\Rightarrow P\nrightarrow Q \]
(53)
\[ P\nrightarrow\left(Q\downarrow R\right)\Leftarrow P\land Q \]
(54)
\[ P\nrightarrow\left(Q\uparrow R\right)\Rightarrow P\land Q \]
(55)
\[ P\nrightarrow\left(Q\nrightarrow R\right)\Leftarrow P\nrightarrow Q \]
(56)
\[ P\nrightarrow\left(Q\nleftarrow R\right)\Leftarrow P\land Q \]
(57)
\[ P\nleftarrow\left(Q\lor R\right)\Leftarrow P\nleftarrow Q \]
(58)
\[ P\nleftarrow\left(Q\land R\right)\Rightarrow P\nleftarrow Q \]
(59)
\[ P\nleftarrow\left(Q\rightarrow R\right)\Leftarrow P\downarrow Q \]
(60)
\[ P\nleftarrow\left(Q\leftarrow R\right)\Leftarrow P\nleftarrow Q \]
(61)
\[ P\nleftarrow\left(Q\downarrow R\right)\Rightarrow P\downarrow Q \]
(62)
\[ P\nleftarrow\left(Q\uparrow R\right)\Leftarrow P\downarrow Q \]
(63)
\[ P\nleftarrow\left(Q\nrightarrow R\right)\Rightarrow P\nleftarrow Q \]
(64)
\[ P\nleftarrow\left(Q\nleftarrow R\right)\Rightarrow P\downarrow Q \]
(1)
\begin{align*} P\lor\left(Q\lor R\right) & \Leftrightarrow P\lor Q\lor R\\ & \Leftarrow P\lor Q \end{align*}
(2)
\begin{align*} P\lor\left(Q\land R\right) & \Leftrightarrow\left(P\lor Q\right)\land\left(P\lor R\right)\\ & \Rightarrow P\lor Q \end{align*}
(3)
\begin{align*} P\lor\left(Q\rightarrow R\right) & \Leftrightarrow P\lor\lnot Q\lor R\\ & \Leftarrow P\leftarrow Q \end{align*}
(4)
\begin{align*} P\lor\left(Q\leftarrow R\right) & \Leftrightarrow P\lor Q\lor\lnot R\\ & \Leftarrow P\lor Q \end{align*}
(5)
\begin{align*} P\lor\left(Q\downarrow R\right) & \Leftrightarrow P\lor\left(\lnot Q\land\lnot R\right)\\ & \Leftrightarrow\left(P\lor\lnot Q\right)\land\left(P\lor\lnot R\right)\\ & \Rightarrow P\leftarrow Q \end{align*}
(6)
\begin{align*} P\lor\left(Q\uparrow R\right) & \Leftrightarrow P\lor\lnot Q\lor\lnot R\\ & \Leftarrow P\leftarrow Q \end{align*}
(7)
\begin{align*} P\lor\left(Q\nrightarrow R\right) & \Leftrightarrow P\lor\left(Q\land\lnot R\right)\\ & \Leftrightarrow\left(P\lor Q\right)\land\left(P\lor\lnot R\right)\\ & \Rightarrow P\lor Q \end{align*}
(8)
\begin{align*} P\lor\left(Q\nleftarrow R\right) & \Leftrightarrow P\lor\left(\lnot Q\land R\right)\\ & \Leftrightarrow\left(P\lor\lnot Q\right)\land\left(P\lor R\right)\\ & \Rightarrow P\leftarrow Q \end{align*}
(9)
\begin{align*} P\land\left(Q\lor R\right) & \Leftrightarrow\left(P\land Q\right)\lor\left(P\land R\right)\\ & \Leftarrow P\land Q \end{align*}
(10)
\begin{align*} P\land\left(Q\land R\right) & \Leftrightarrow P\land Q\land R\\ & \Rightarrow P\land Q \end{align*}
(11)
\begin{align*} P\land\left(Q\rightarrow R\right) & \Leftrightarrow P\land\left(\lnot Q\lor R\right)\\ & \Leftrightarrow\left(P\land\lnot Q\right)\lor\left(P\land R\right)\\ & \Leftarrow P\nrightarrow Q \end{align*}
(12)
\begin{align*} P\land\left(Q\leftarrow R\right) & \Leftrightarrow P\land\left(Q\lor\lnot R\right)\\ & \Leftrightarrow\left(P\land Q\right)\lor\left(P\land\lnot R\right)\\ & \Leftarrow P\land Q \end{align*}
(13)
\begin{align*} P\land\left(Q\downarrow R\right) & \Leftrightarrow P\land\lnot Q\land\lnot R\\ & \Rightarrow P\nrightarrow Q \end{align*}
(14)
\begin{align*} P\land\left(Q\uparrow R\right) & \Leftrightarrow P\land\left(\lnot Q\lor\lnot R\right)\\ & \Leftrightarrow\left(P\land\lnot Q\right)\lor\left(P\land\lnot R\right)\\ & \Leftarrow P\nrightarrow Q \end{align*}
(15)
\begin{align*} P\land\left(Q\nrightarrow R\right) & \Leftrightarrow P\land Q\land\lnot R\\ & \Rightarrow P\land Q \end{align*}
(16)
\begin{align*} P\land\left(Q\nleftarrow R\right) & \Leftrightarrow P\land\lnot Q\land R\\ & \Rightarrow P\nrightarrow Q \end{align*}
(17)
\begin{align*} P\rightarrow\left(Q\lor R\right) & \Leftrightarrow\lnot P\lor Q\lor R\\ & \Leftarrow P\rightarrow Q \end{align*}
(18)
\begin{align*} P\rightarrow\left(Q\land R\right) & \Leftrightarrow\lnot P\lor\left(Q\land R\right)\\ & \Leftrightarrow\left(\lnot P\lor Q\right)\land\left(\lnot P\lor R\right)\\ & \Rightarrow P\rightarrow Q \end{align*}
(19)
\begin{align*} P\rightarrow\left(Q\rightarrow R\right) & \Leftrightarrow\lnot P\lor\lnot Q\lor R\\ & \Leftarrow P\uparrow Q \end{align*}
(20)
\begin{align*} P\rightarrow\left(Q\leftarrow R\right) & \Leftrightarrow\lnot P\lor Q\lor\lnot R\\ & \Leftarrow P\rightarrow Q \end{align*}
(21)
\begin{align*} P\rightarrow\left(Q\downarrow R\right) & \Leftrightarrow\lnot P\lor\left(\lnot Q\land\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\lor\lnot Q\right)\land\left(\lnot P\lor\lnot R\right)\\ & \Rightarrow P\uparrow Q \end{align*}
(22)
\begin{align*} P\rightarrow\left(Q\uparrow R\right) & \Leftrightarrow\lnot P\lor\lnot Q\lor\lnot R\\ & \Leftarrow P\uparrow Q \end{align*}
(23)
\begin{align*} P\rightarrow\left(Q\nrightarrow R\right) & \Leftrightarrow\lnot P\lor\left(Q\land\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\lor Q\right)\land\left(\lnot P\lor\lnot R\right)\\ & \Rightarrow P\rightarrow Q \end{align*}
(24)
\begin{align*} P\rightarrow\left(Q\nleftarrow R\right) & \Leftrightarrow\lnot P\lor\left(\lnot Q\land R\right)\\ & \Leftrightarrow\left(\lnot P\lor\lnot Q\right)\land\left(\lnot P\lor R\right)\\ & \Rightarrow P\uparrow Q \end{align*}
(25)
\begin{align*} P\leftarrow\left(Q\lor R\right) & \Leftrightarrow P\lor\lnot\left(Q\lor R\right)\\ & \Leftrightarrow P\lor\left(\lnot Q\land\lnot R\right)\\ & \Leftrightarrow\left(P\lor\lnot Q\right)\land\left(P\lor\lnot R\right)\\ & \Rightarrow P\leftarrow Q \end{align*}
(26)
\begin{align*} P\leftarrow\left(Q\land R\right) & \Leftrightarrow P\lor\lnot\left(Q\land R\right)\\ & \Leftrightarrow P\lor\lnot Q\lor\lnot R\\ & \Leftarrow P\leftarrow Q \end{align*}
(27)
\begin{align*} P\leftarrow\left(Q\rightarrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\rightarrow R\right)\\ & \Leftrightarrow P\lor\left(Q\land\lnot R\right)\\ & \Leftrightarrow\left(P\lor Q\right)\land\left(P\lor\lnot R\right)\\ & \Rightarrow P\lor Q \end{align*}
(28)
\begin{align*} P\leftarrow\left(Q\leftarrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\leftarrow R\right)\\ & \Leftrightarrow P\lor\left(\lnot Q\land R\right)\\ & \Leftrightarrow\left(P\lor\lnot Q\right)\\ & \Rightarrow P\leftarrow Q \end{align*}
(29)
\begin{align*} P\leftarrow\left(Q\downarrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\downarrow R\right)\\ & \Leftrightarrow P\lor Q\lor R\\ & \Leftarrow P\lor Q \end{align*}
(30)
\begin{align*} P\leftarrow\left(Q\uparrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\uparrow R\right)\\ & \Leftrightarrow P\lor\left(Q\land R\right)\\ & \Leftrightarrow\left(P\lor Q\right)\land\left(P\lor R\right)\\ & \Rightarrow P\lor Q \end{align*}
(31)
\begin{align*} P\leftarrow\left(Q\nrightarrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\nrightarrow R\right)\\ & \Leftrightarrow P\lor\lnot Q\lor R\\ & \Leftarrow P\leftarrow Q \end{align*}
(32)
\begin{align*} P\leftarrow\left(Q\nleftarrow R\right) & \Leftrightarrow P\lor\lnot\left(Q\nleftarrow R\right)\\ & \Leftrightarrow P\lor Q\lor\lnot R\\ & \Leftarrow P\lor Q \end{align*}
(33)
\begin{align*} P\downarrow\left(Q\lor R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\lor R\right)\\ & \Leftrightarrow\lnot P\land\lnot Q\land\lnot R\\ & \Rightarrow P\downarrow Q \end{align*}
(34)
\begin{align*} P\downarrow\left(Q\land R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\land R\right)\\ & \Leftrightarrow\lnot P\land\left(\lnot Q\lor\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\land\lnot Q\right)\lor\left(\lnot P\land\lnot R\right)\\ & \Leftarrow P\downarrow Q \end{align*}
(35)
\begin{align*} P\downarrow\left(Q\rightarrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\rightarrow R\right)\\ & \Leftrightarrow\lnot P\land Q\land\lnot R\\ & \Rightarrow P\nleftarrow Q \end{align*}
(36)
\begin{align*} P\downarrow\left(Q\leftarrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\leftarrow R\right)\\ & \Leftrightarrow\lnot P\land\lnot Q\land R\\ & \Rightarrow P\downarrow Q \end{align*}
(37)
\begin{align*} P\downarrow\left(Q\downarrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\downarrow R\right)\\ & \Leftrightarrow\lnot P\land\left(Q\lor R\right)\\ & \Leftrightarrow\left(\lnot P\land Q\right)\lor\left(\lnot P\land R\right)\\ & \Leftarrow P\nleftarrow Q \end{align*}
(38)
\begin{align*} P\downarrow\left(Q\uparrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\uparrow R\right)\\ & \Leftrightarrow\lnot P\land Q\land R\\ & \Rightarrow P\nleftarrow Q \end{align*}
(39)
\begin{align*} P\downarrow\left(Q\nrightarrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\nrightarrow R\right)\\ & \Leftrightarrow\lnot P\land\left(\lnot Q\lor R\right)\\ & \Leftrightarrow\left(\lnot P\land\lnot Q\right)\lor\left(\lnot P\land R\right)\\ & \Leftarrow P\downarrow Q \end{align*}
(40)
\begin{align*} P\downarrow\left(Q\nleftarrow R\right) & \Leftrightarrow\lnot P\land\lnot\left(Q\nleftarrow R\right)\\ & \Leftrightarrow\lnot P\land\left(Q\lor\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\land Q\right)\lor\left(\lnot P\land\lnot R\right)\\ & \Leftarrow P\nleftarrow Q \end{align*}
(41)
\begin{align*} P\uparrow\left(Q\lor R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\lor R\right)\\ & \Leftrightarrow\lnot P\lor\left(\lnot Q\land\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\lor\lnot Q\right)\land\left(\lnot P\lor\lnot R\right)\\ & \Rightarrow P\uparrow Q \end{align*}
(42)
\begin{align*} P\uparrow\left(Q\land R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\land R\right)\\ & \Leftrightarrow\lnot P\lor\lnot Q\lor\lnot R\\ & \Leftarrow P\uparrow Q \end{align*}
(43)
\begin{align*} P\uparrow\left(Q\rightarrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\rightarrow R\right)\\ & \Leftrightarrow\lnot P\lor\left(Q\land\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\lor Q\right)\land\left(\lnot P\lor\lnot R\right)\\ & \Rightarrow P\rightarrow Q \end{align*}
(44)
\begin{align*} P\uparrow\left(Q\leftarrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\leftarrow R\right)\\ & \Leftrightarrow\lnot P\lor\left(\lnot Q\land R\right)\\ & \Leftrightarrow\left(\lnot P\lor\lnot Q\right)\land\left(\lnot P\lor R\right)\\ & \Rightarrow P\uparrow Q \end{align*}
(45)
\begin{align*} P\uparrow\left(Q\downarrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\downarrow R\right)\\ & \Leftrightarrow\lnot P\lor Q\lor R\\ & \Leftarrow P\rightarrow Q \end{align*}
(46)
\begin{align*} P\uparrow\left(Q\uparrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\uparrow R\right)\\ & \Leftrightarrow\lnot P\lor\left(Q\land R\right)\\ & \Leftrightarrow\left(\lnot P\lor Q\right)\land\left(\lnot P\lor R\right)\\ & \Rightarrow P\rightarrow Q \end{align*}
(47)
\begin{align*} P\uparrow\left(Q\nrightarrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\nrightarrow R\right)\\ & \Leftrightarrow\lnot P\lor\lnot Q\lor R\\ & \Leftarrow P\uparrow Q \end{align*}
(48)
\begin{align*} P\uparrow\left(Q\nleftarrow R\right) & \Leftrightarrow\lnot P\lor\lnot\left(Q\nleftarrow R\right)\\ & \Leftrightarrow\lnot P\lor Q\lor\lnot R\\ & \Leftarrow P\rightarrow Q \end{align*}
(49)
\begin{align*} P\nrightarrow\left(Q\lor R\right) & \Leftrightarrow P\land\lnot\left(Q\lor R\right)\\ & \Leftrightarrow P\land\lnot Q\land\lnot R\\ & \Rightarrow P\nrightarrow Q \end{align*}
(50)
\begin{align*} P\nrightarrow\left(Q\land R\right) & \Leftrightarrow P\land\lnot\left(Q\land R\right)\\ & \Leftrightarrow P\land\left(\lnot Q\lor\lnot R\right)\\ & \Leftrightarrow\left(P\land\lnot Q\right)\lor\left(P\land\lnot R\right)\\ & \Leftarrow P\nrightarrow Q \end{align*}
(51)
\begin{align*} P\nrightarrow\left(Q\rightarrow R\right) & \Leftrightarrow P\land\lnot\left(Q\rightarrow R\right)\\ & \Leftrightarrow P\land Q\land\lnot R\\ & \Rightarrow P\land Q \end{align*}
(52)
\begin{align*} P\nrightarrow\left(Q\leftarrow R\right) & \Leftrightarrow P\land\lnot\left(Q\leftarrow R\right)\\ & \Leftrightarrow P\land\lnot Q\land R\\ & \Rightarrow P\nrightarrow Q \end{align*}
(53)
\begin{align*} P\nrightarrow\left(Q\downarrow R\right) & \Leftrightarrow P\land\lnot\left(Q\downarrow R\right)\\ & \Leftrightarrow P\land\left(Q\lor R\right)\\ & \Leftrightarrow\left(P\land Q\right)\lor\left(P\land R\right)\\ & \Leftarrow P\land Q \end{align*}
(54)
\begin{align*} P\nrightarrow\left(Q\uparrow R\right) & \Leftrightarrow P\land\lnot\left(Q\uparrow R\right)\\ & \Leftrightarrow P\land Q\land R\\ & \Rightarrow P\land Q \end{align*}
(55)
\begin{align*} P\nrightarrow\left(Q\nrightarrow R\right) & \Leftrightarrow P\land\lnot\left(Q\nrightarrow R\right)\\ & \Leftrightarrow P\land\left(\lnot Q\lor R\right)\\ & \Leftrightarrow\left(P\land\lnot Q\right)\lor\left(P\land R\right)\\ & \Leftarrow P\nrightarrow Q \end{align*}
(56)
\begin{align*} P\nrightarrow\left(Q\nleftarrow R\right) & \Leftrightarrow P\land\lnot\left(Q\nleftarrow R\right)\\ & \Leftrightarrow P\land\left(Q\lor\lnot R\right)\\ & \Leftrightarrow\left(P\land Q\right)\lor\left(P\land\lnot R\right)\\ & \Leftarrow P\land Q \end{align*}
(57)
\begin{align*} P\nleftarrow\left(Q\lor R\right) & \Leftrightarrow\lnot P\land\left(Q\lor R\right)\\ & \Leftrightarrow\left(\lnot P\land Q\right)\lor\left(\lnot P\land R\right)\\ & \Leftarrow P\nleftarrow Q \end{align*}
(58)
\begin{align*} P\nleftarrow\left(Q\land R\right) & \Leftrightarrow\lnot P\land Q\land R\\ & \Rightarrow P\nleftarrow Q \end{align*}
(59)
\begin{align*} P\nleftarrow\left(Q\rightarrow R\right) & \Leftrightarrow\lnot P\land\left(\lnot Q\lor R\right)\\ & \Leftrightarrow\left(\lnot P\land\lnot Q\right)\lor\left(\lnot P\land R\right)\\ & \Leftarrow P\downarrow Q \end{align*}
(60)
\begin{align*} P\nleftarrow\left(Q\leftarrow R\right) & \Leftrightarrow\lnot P\land\left(Q\lor\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\land Q\right)\lor\left(\lnot P\land\lnot R\right)\\ & \Leftarrow P\nleftarrow Q \end{align*}
(61)
\begin{align*} P\nleftarrow\left(Q\downarrow R\right) & \Leftrightarrow\lnot P\land\lnot Q\land\lnot R\\ & \Rightarrow P\downarrow Q \end{align*}
(62)
\begin{align*} P\nleftarrow\left(Q\uparrow R\right) & \Leftrightarrow\lnot P\land\left(\lnot Q\lor\lnot R\right)\\ & \Leftrightarrow\left(\lnot P\land\lnot Q\right)\lor\left(\lnot P\land\lnot R\right)\\ & \Leftarrow P\downarrow Q \end{align*}
(63)
\begin{align*} P\nleftarrow\left(Q\nrightarrow R\right) & \Leftrightarrow\lnot P\land Q\land\lnot R\\ & \Rightarrow P\nleftarrow Q \end{align*}
(64)
\begin{align*} P\nleftarrow\left(Q\nleftarrow R\right) & \Leftrightarrow\lnot P\land\lnot Q\land R\\ & \Rightarrow P\downarrow Q \end{align*}
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タイトル | 3つのうち1つを消したものとの包含関係 |
URL | https://www.nomuramath.com/r14f2zuh/ |
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