#### Question

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

p ∨ ( ~q ∨ r )

~p ∧ ( q → r )

~p ∧ ( ~q → ~r )

~p ∨ ( q ∧ ~r )

#### 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 ) **

Is there an error in this question or solution?

#### APPEARS IN

Solution The negation of p ∧ (q → r) is Concept: Mathematical Logic - Algebra of Statements.