Question

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

Options

• p ∨ ( ~q ∨ r )

• ~p ∧ ( q → r )

• ~p ∧ ( ~q → ~r )

• ~p ∨ ( q ∧ ~r )

Answer 1

~ [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 )