Question: using a truth table show that two propositions p ...
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Using a truth table show that two propositions
(p → q) ∧ (~p → q),and
p ⊕ q
note: ⊕ = exclusive disjunction symbol.

are not equivalent. (i.e show that (p → q) ∧ (~p → q) ≠ p ⊕ q

Using equivalence laws of propositional logic, show that (p ∧ q) → (p ∨ q)
is a tautology

Using equivalence laws of propositional logic, show that ~(p v (~p ^ q)) ≡ ~p ^ ~q

Using equivalence laws of propositional logic, show that (p ∧ q ∧ ¬r) ∨ (p ∧ ¬q ∧ ~r) ≡ p ∧ ~r