写像と集合の演算
\[
f\left(A_{1}\cup A_{2}\right)=f\left(A_{1}\right)\cup f\left(A_{2}\right)
\]
写像と論理和・論理積
\[
\bigvee_{x\in X}\bigwedge_{\lambda\in\Lambda}x\in A_{\lambda},y=f\left(x\right)\Rightarrow\bigwedge_{\lambda\in\Lambda}\bigvee_{x\in X}x\in A_{\lambda},y=f\left(x\right)
\]
像・逆像と補集合の関係
\[
f^{\bullet}\left(B^{c}\right)=\left(f^{\bullet}\left(B\right)\right)^{c}
\]
逆像の元と像の元
\[
a\in f^{\bullet}\left(B\right)\Leftrightarrow f\left(a\right)\in B
\]