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Which of the following logical consequences are correct?

  1. $(p \rightarrow q) |= \neg p \rightarrow \neg q$
  2. $(p \rightarrow q) \wedge \neg q |= \neg p$
  3. $p \rightarrow q \wedge r |= (p \rightarrow q) \rightarrow r$
  4. $p \vee (\neg q \wedge r) |= q \vee \neg r \rightarrow p$
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$\text{X} \models \text{Y}$ if and only if $\text{X}$ implies $\text{Y}$ i.e., $\text{X} \rightarrow \text{Y}$ is true.

B; D are correct.

A is incorrect because when $p$ is false, $q$ is true, then A is false.

C is false when $r$ is false, and $p$ is false.

Detailed Video Solution:

https://youtu.be/nclBhBmtz2g?t=5405

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