Verified Solution • 2025–26 Session moderate

QJEEM22Ma7e90: JEE Main 2022 Mathematics - Class 11 JEEM22Ma7e90 Solution: The statement is NOT equivalent to

The statement (p⇒q)∨(p⇒r)(p \Rightarrow q) \vee(p \Rightarrow r) is NOT equivalent to

Multiple Choice Options

  • A (p∧(∼r))⇒q(p \wedge(\sim r)) \Rightarrow q
  • B (∼q)⇒((∼r)∨p)(\sim q) \Rightarrow((\sim r) \vee p)
  • C p⇒(q∨r)p \Rightarrow(q \vee r)
  • D (p∧(∼q))⇒r(p \wedge(\sim q)) \Rightarrow r

Step-by-Step Verified Solution

(A)(p∧(∼r))⇒q(\mathrm{A})(p \wedge(\sim r)) \Rightarrow q

amp;∼(p∧∼r)∨qamp;≡(∼p∨r)∨qamp;≡∼p∨(r∨q)amp;≡p→(q∨r)amp;≡(p⇒q)∨(p⇒r)\begin{aligned}&\sim(p \wedge \sim r) \vee q \\\\&\equiv(\sim p \vee r) \vee q \\\\&\equiv \sim p \vee(r \vee q) \\\\&\equiv p \rightarrow(q \vee r) \\\\&\equiv(p \Rightarrow q) \vee(p \Rightarrow r)\end{aligned}

(C) p⇒(q∨r)p \Rightarrow(q \vee r)

amp;≡∼p∨(q∨r)amp;≡(∼p∨q)∨(∼p∨r)amp;≡(p→q)∨(p→r)\begin{aligned}&\equiv \sim p \vee(q \vee r) \\\\&\equiv(\sim p \vee q) \vee(\sim p \vee r) \\\\&\equiv(p \rightarrow q) \vee(p \rightarrow r)\end{aligned}

(D) (p∧∼q)⇒r(p \wedge \sim q) \Rightarrow r

≡p⇒(q∨r)\equiv p \Rightarrow(q \vee r)

amp;≡(p⇒q)∨(p⇒r)\begin{aligned}& \equiv(p \Rightarrow q) \vee(p \Rightarrow r)\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring