Verified Solution • 2025–26 Session moderate

QJEEM23Ma7c7c: JEE Main 2023 Mathematics - Class 11 JEEM23Ma7c7c Solution: Statement is logically equivalent to :

Statement (P⇒Q)∧(R⇒Q)\mathrm{(P \Rightarrow Q) \wedge(R \Rightarrow Q)} is logically equivalent to :

Multiple Choice Options

  • A (P⇒R)∧(Q⇒R)(P \Rightarrow R) \wedge(Q \Rightarrow R)
  • B (P⇒R)∨(Q⇒R)(P \Rightarrow R) \vee(Q \Rightarrow R)
  • C (P∧R)⇒Q(P \wedge R) \Rightarrow Q
  • D (P∨R)⇒Q(P \vee R) \Rightarrow Q

Step-by-Step Verified Solution

We have, (P⇒Q)∧(R⇒Q)(P \Rightarrow Q) \wedge(R \Rightarrow Q)

amp;≡(∼P∨Q)∧(∼R∨Q)amp;≡(∼P∧∼R)∨Q (by distributive law) amp;≡∼(P∨R)∨Qamp;≡(P∨R)⇒Q\begin{aligned}& \equiv(\sim P \vee Q) \wedge(\sim R \vee Q) \\\\& \equiv(\sim P \wedge \sim R) \vee Q \text { (by distributive law) }\\\\& \equiv \sim(P \vee R) \vee Q \\\\& \equiv(P \vee R) \Rightarrow Q\end{aligned}

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