Let $p, q, r$ be three logical statements. Consider the compound statements $S_1:((\sim p) \vee q) \vee((\sim p) \vee r)$ and $S_2: p \rightarrow(q \vee r)$ Then, which of the following is NOT true?

• A

  If $S_2$ is true, then $S_1$ is true
• B

  If $S_2$ is false, then $S_1$ is false
• Correct answer
  C

  If $S_2$ is false, then $S_1$ is true
• D

  If $S_1$ is false, then $S_2$ is false

Hence, the correct answer is option: 'C'.