Maharashtra State BoardHSC Arts 12th Board Exam
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The negation of p ∧ (q → r) is - Mathematics and Statistics

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MCQ

The negation of p ∧ (q → r) is ______________.

Options

  • p ∨ ( ~q ∨ r )

  • ~p ∧ ( q → r )

  • ~p ∧ ( ~q → ~r )

  • ~p ∨ ( q ∧ ~r )

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Solution

~ [P ∧ (q → r)

=~[( P)] ∨ [~ (q → r)]                             ...(By De Morgan's law)
=~[( P)] ∨ [~ (~q ∨ r )]                           ...(By Conditional Law)
=~[( P)] ∨ [( q ∧ ~r )]                             ...(By De Morgan's law)

~ [ P ∧ ( q → r )] = ~ P ∨ ( q ∧ ~r ) 

Concept: Algebra of Statements
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