Verified Solution • 2025–26 Session moderate

QJEEM23Mab3e1: JEE Main 2023 Mathematics - Class 11 JEEM23Mab3e1 Solution: The negation of the statement is

The negation of the statement ((A∧(B∨C))⇒(A∨B))⇒A((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A is

Multiple Choice Options

  • A equivalent to B ∨∼CB ~\vee \sim C
  • B equivalent to ∼A\sim A
  • C equivalent to ∼C\sim C
  • D a fallacy

Step-by-Step Verified Solution

((A∧(B∨C))⇒(A∨B))⇒A((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A

≡\equiv [∼(A∧(B∨C))∨(A∨B)]⇒A[\sim(\mathrm{A} \wedge(\mathrm{B} \vee \mathrm{C})) \vee(\mathrm{A} \vee \mathrm{B})] \Rightarrow \mathrm{A}

≡\equiv ∼(∼(A∧(B∨C))∨(A∨B))∨A\sim(\sim(A \wedge(B \vee C)) \vee(A \vee B)) \vee A

≡\equiv (A∧(B∨C))∧∼(A∨B)∨A(A \wedge(B \vee C)) \wedge \sim(A \vee B) \vee A

≡\equiv (f∨A)=A(f \vee A)=A

∴ Negation of statement =∼A\therefore \text { Negation of statement }=\sim A

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