Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.
Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r)...
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
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.
Show that ~p -> (q -> r) and q-> (p v r) are logically equivalent
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.
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
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
A Theorem 3.2. Suppose P, R and S are atomic propositions. Then the propositional form appearing in column A is logically equivalent to the corre- sponding propositional form in Column B. В. POR ( P R ) ^ (R=P). ~(PvR) (~P) ^ (~ R) ~(PAR) (~ P) v (~ R) ~( PR) P^~R ~(PAR) P=R P^(RVS) (PAR) v (PAS) Pv(RAS) (P v R) ^ (PVS) While the importance of the equivalent propositional forms stated in The- orem 3.2 are important,...
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.
3. (10 pts.) Use logical equivalences to show that (p r)v(q r) and (pAq) r ane logically equivalent.