Verified Solution • 2025–26 Session moderate

QJEEM21Mae57e: JEE Main 2021 Mathematics - Class 11 JEEM21Mae57e Solution: The statement A (B A) is equivalent to :

The statement A →\to (B →\to A) is equivalent to :

Multiple Choice Options

  • A A →\to (A ⟷\mathrel{\mathop{\kern0pt\longleftrightarrow}\limits_{}} B)
  • B A →\to (A ∨\vee B)
  • C A →\to (A ∧\wedge B)
  • D A →\to (A →\to B)

Step-by-Step Verified Solution

A→(B→A)A \to (B \to A)

⇒A→(∼B∨A)\Rightarrow A \to ( \sim B \vee A)

⇒ ∼A∨(∼B∨A)\Rightarrow \, \sim A \vee ( \sim B \vee A)

⇒ ∼B∨(∼A∨A)\Rightarrow \, \sim B \vee ( \sim A \vee A)

⇒ ∼B∨t\Rightarrow \, \sim B \vee t

= t (tantology)

From options :

(B) A→(A∨B)A \to (A \vee B)

⇒ ∼A∨(A∨B)\Rightarrow \, \sim A \vee (A \vee B)

⇒(∼A∨A)∨B\Rightarrow ( \sim A \vee A) \vee B

⇒t∨B\Rightarrow t \vee B

⇒t\Rightarrow t

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