Question

以下哪一项与“若 $P$ 为真，则 $Q$ 为假”等价？

Which of the following is equivalent to “If $P$ is true then $Q$ is false”?

“ $P$ 为真，或 $Q$ 为假。”

“ $P$ is true or $Q$ is false.”

“若 $Q$ 为假，则 $P$ 为真。”

“If $Q$ is false then $P$ is true.”

“若 $P$ 为假，则 $Q$ 为真。”

“If $P$ is false then $Q$ is true.”

“若 $Q$ 为真，则 $P$ 为假。”

“If $Q$ is true then $P$ is false.”

“若 $Q$ 为真，则 $P$ 为真。”

“If $Q$ is true then $P$ is true.”

一个命题与其逆否命题等价

An implication is equivalent to its contrapositive

将蕴含方向反转，并分别否定“ $P$ 为真”和“ $Q$ 为假”

Reverse the implication and negate both “ $P$ true” and “ $Q$ false”

“ $P$ 为真蕴含 $Q$ 为假”的逆否命题是“ $Q$ 不为假蕴含 $P$ 不为真”。这正是“若 $Q$ 为真，则 $P$ 为假”。

因此，正确答案是 D。

The contrapositive of “ $P$ true implies $Q$ false” is “ $Q$ not false implies $P$ not true.” This is exactly “If $Q$ is true then $P$ is false.”

Therefore, the correct answer is D.