Verified Solution • 2025–26 Session moderate

QJEEM22Ma4d82: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4d82 Solution: Let p, q, r be three logical statements. Consider the compound…

Let p, q, r be three logical statements. Consider the compound statements

S1:((∼p)∨q)∨((∼p)∨r){S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r) and

S2:p→(q∨r){S_2}:p \to (q \vee r)

Then, which of the following is NOT true?

Multiple Choice Options

  • A If S2 is True, then S1 is True
  • B If S2 is False, then S1 is False
  • C If S2 is False, then S1 is True
  • D If S1 is False, then S2 is False

Step-by-Step Verified Solution

S1:(∼p∨q)∨(∼p∨r){S_1}:( \sim p \vee q) \vee ( \sim p \vee r)

≅(∼p∨q∨r)\cong ( \sim p \vee q \vee r)

S2:∼p∨(q∨r){S_2}: \sim p \vee (q \vee r)

Both are same

So, option (C) is incorrect.

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