Discrete Math:
Decide whether (p^q)r and (pr)^(qr) are logically equivalent using boolean algebra. Show work! Do NOT use truth table.
Discrete Math: Decide whether (p^q)r and (pr)^(qr) are logically equivalent using boolean algebra. Show work! Do...
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.
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
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.
WITHOUT constructing TT Show whether or not p-, q ^ (q-r)-p-, r is logically equivalent to
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
Problem 12.1: Let p and be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work! Circle one: A: The statements are equivalent. B: The statements are not equivalent. Problem 12.2: Let P, Q, and be be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work! Circle one: A: The statements are equivalent. B: The statements are not equivalent.
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?
4. Use truth tables to determine whether the following two statements are logically equivalent. (P+Q)^(~Q) and ~ (PVQ)
Using FTLM. a) Let . Use linear algebra to prove that there is a polynomial such that p + p' - 3p'' = q. Hint: consider the map defined by Tp: p + p' - 3p'', and use FTLM. b) Let be distinct elements of . Let be any elements of . Use linear algebra to prove that there is a such that Hint: consider the map defined by . You can use any facts from algebra about the solution...