Show that (r ∨ p) ∧ [(∼ r ∨ (p ∧ q)) ∧ (r ∨ q)] ≡ p ∧ q.
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.
Question: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.
p implies r q implies r conclusion (p or q ) implies r show they sre logical equivalent (pVa) (pVa)
Show that ~p -> (q -> r) and q-> (p v r) are logically equivalent
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
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.
Problem 3.11 Show using a chain of logical equivalences that (p → r)A(q → r) pv q) →
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?
How many of the disjunctions p∨¬q, ¬p∨q, q ∨r, q ∨¬ r, and ¬q ∨¬ r can be made simultaneously true by an assignment of truth values to p, q, and r? Please explain how to find that? thinking process!
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