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Question: Answered & Verified by Expert
Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ denote arbitrary statements. Then the logically equivalent of the statement $\mathrm{p} \Rightarrow(\mathrm{q} \vee \mathrm{r})$ is:
MathematicsMathematical ReasoningJEE MainJEE Main 2014 (12 Apr Online)
Options:
  • A
    $(\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}$
  • B
    $(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{p} \Rightarrow \mathrm{r})$
  • C
    $(\mathrm{p} \Rightarrow \sim \mathrm{q}) \wedge(\mathrm{p} \Rightarrow \mathrm{r})$
  • D
    $(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{p} \Rightarrow \sim \mathrm{r})$
Solution:
2359 Upvotes Verified Answer
The correct answer is:
$(\mathrm{p} \Rightarrow \mathrm{q}) \vee(\mathrm{p} \Rightarrow \mathrm{r})$
Given statement is
$p \Rightarrow(q \vee r)$ which is equivalent to
$$
(p \Rightarrow q) \vee(p \Rightarrow r)
$$

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