Verified Solution • 2025–26 Session moderate

QJEEM23Maf48a: JEE Main 2023 Mathematics - Class 11 JEEM23Maf48a Solution: The converse of is

The converse of ((∼p)∧q)⇒r((\sim p) \wedge q) \Rightarrow r is

Multiple Choice Options

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

Step-by-Step Verified Solution

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

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