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Question: Answered & Verified by Expert
If $p, q, r$ are simple propositions, then $(p \wedge q) \wedge(q \wedge r)$ is true then
MathematicsMathematical ReasoningJEE Main
Options:
  • A $p, q, r$ are all false
  • B $p, q, r$ are all true
  • C $p, q$ are true and $r$ is false
  • D $p$ is true and $q$ and $r$ are false
Solution:
1508 Upvotes Verified Answer
The correct answer is: $p, q, r$ are all true
$(p \wedge q) \wedge(q \wedge r)$ is true means $p \wedge q, q \wedge r$ are both true. $\Rightarrow p, q, r$ are all true.

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