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JEE Main 202127 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2021 · 27 August · Evening Shift · Mathematics · Mathematical Reasoning

The Boolean expression ( p ∧ q ) ⇒ ( (r ∧ q) ∧ p) is equivalent to:

The Boolean expression (p∧q)⇒( p ∧ q ) ⇒\left(\left(r ∧ q\right) ∧ p\right) is equivalent to:

Options

  1. A(p∧r)⇒(p∧q)( p ∧ r ) ⇒ ( p ∧ q )
  2. B(q∧r)⇒(p∧q)( q ∧ r ) ⇒ ( p ∧ q )
  3. C(p∧q)⇒(r∧q)( p ∧ q ) ⇒ ( r ∧ q )
  4. D(p∧q)⇒(r∨q)( p ∧ q ) ⇒ ( r ∨ q )

Correct answer

C. (p∧q)⇒(r∧q)( p ∧ q ) ⇒ ( r ∧ q )

Step-by-step solution

(p∧q)⇒((r∧q)∧p)≡(p∧q)⇒(r∧(p∧q))…….(i)( p ∧ q ) ⇒ ( ( r ∧ q ) ∧ p ) ≡ ( p ∧ q ) ⇒ ( r ∧ ( p ∧ q ) ) \ldots \ldots . ( i )

Case: II when p∧q=Tp ∧ q = T and r=Fr = F

Statement−(i)- ( i ) is false as well as option (3)( 3 ) is also false
option (1),( 1 ) , option (2)( 2 ) are True so given expression is not equivalent to option (1)( 1 ), option (2)( 2 )

option (4)( 4 ) may be true if we consider q=T∴q = T ∴ option (4)( 4 ) is also not equivalent to option (1)( 1 ) Case : IIII p∧q=p ∧ q =False

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