MHT CET · Maths · Mathematical Reasoning
The logical expression
\([\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{r})]\) is equivalent to
- A \(\mathrm{p}\)
- B \(\mathrm{q}\)
- C \(\mathrm{p} \wedge \mathrm{r}\)
- D \(\mathrm{q} \vee \mathrm{r}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{q} \vee \mathrm{r}\)
Step-by-step Solution
Detailed explanation
\([p \wedge(q \vee r)] \vee[(\sim p \wedge q) \vee(\sim p \wedge r)]\)
\(\equiv[p \wedge(q \vee r)] \vee[\sim p \wedge(q \vee r)]\)
\(\equiv(q \vee r) \wedge(p \vee \sim p)\)
\(\equiv(q \vee r) \wedge T\)
\(\equiv q \vee r\)
\(\equiv[p \wedge(q \vee r)] \vee[\sim p \wedge(q \vee r)]\)
\(\equiv(q \vee r) \wedge(p \vee \sim p)\)
\(\equiv(q \vee r) \wedge T\)
\(\equiv q \vee r\)
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