1. Logics

and 逻辑与

\(P\) and \(Q\) is true if both \(P\) and \(Q\) are true and false otherwise.

仅 \(P\) 与 \(Q\) 均为真的时候表达式的值为真。

or 逻辑或

\(P\) or \(Q\) is true in all cases except when both \(P\) and \(Q\) are false.

仅 \(P\) 与 \(Q\) 均为假的时候表达式的值为假。

implies 逻辑蕴含

"\(P\) implies \(Q\)" is also written as "if \(P\), and \(Q\)", "\(P \Rightarrow Q\)"
It's false if \(P\) is true and \(Q\) is false; it is true in all other cases.

仅 \(P\) 为真且 \(Q\) 为假的时候表达式的值为假。

if and only if 逻辑等价

"\(P\) if and only if \(Q\)" is also written as "\(P\) implies \(Q\) and \(Q\) implies \(P\)", "\(P \Leftrightarrow Q\)"
It's true exactly when \(P\) and \(Q\) are both true or both false.

\(P\) 与 \(Q\) 均为真或均为假时表达式的值为真。

not 逻辑非

It is not the case that P. It's true if and only if P is false.

仅 \(P\) 为假的时候表达式的值为真。