Question

Build a complete truth table and Show that they are Logically equivalent

¬(¬P ∧ Q) ∧ (P ∨Q)≡ p

Answer 1

Solution:

LHS$=¬(¬P ∧ Q) ∧ (P ∨Q)$

Truth table:

RHS$=P$

Truth table:

Thus, $¬(¬P ∧ Q) ∧ (P ∨Q)≡ P$ are logically equivalent.