Show that ~p -> (q -> r) and q-> (p v r) are logically equivalent
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Show that ~p -> (q -> r ) and q -> (p v r) are logically equivalent using laws
2. (a) Show that (PVQ) + R is not logically equivalent to (P + R) V(Q + R) using a truth table. (b) Is (PAQ) → R logically equivalent to (P + R) A( Q R )? If so, use a truth table to establish this. If not, show that it is false.
6. Maximum score 3 ( 1 per part).Show that:(b) (p → q) → r and p →(q → r) are not logically equivalent.(c) p ↔ q and ¬ p ↔ ¬ q are logically equivalent.
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
5 points Show that p + (q + r) and q + (pvr) are logically equivalent without using a truth table. To get full credit, include which logical equivalences you used.
How do you show the following propositions are logically equivalent? (a) [(p → q) → r] ⊕ (p ∧ q ∧ r) and (p ∨ r) ⊕ (p ∧ q) (b) ¬∃x {P(x) → ∃y [Q(x, y) ⊕ R(x, y)] } and (∀x P(x)) ∧ [∀x ∀y(Q(x, y) ↔ R(x, y))] (c) Does [(p → q) ∧ (q → r)] → r implies (p → r) → r?
QUESTION 23 The statements P + (Q v R) and (P +Q) v (P + R) are logically equivalent. True False QUESTION 24 The statements (P^Q) + Rand (P + R)^(Q + R) are logically equivalent. True False QUESTION 25 ( PQ) and PA-Q are logically equivalent statements True False QUESTION 26 According to De Morgan's Laws, (PAQ) is logically equivalent to 7P ^ 70. True False
Discrete math problems: 9. Show that p = 10. Show that p = q and ( q p = n are logically equivalent. ) and q = (p V r) are logically equivalent. r
3. (10 pts.) Use logical equivalences to show that (p r)v(q r) and (pAq) r ane logically equivalent.
Discrete Math: Decide whether (p^q)r and (pr)^(qr) are logically equivalent using boolean algebra. Show work! Do NOT use truth table. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.