7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P ^ Q)] ^ [P ^ (P ^ Q)]} b) B = {[¬(P ^ S)V ¬Q] ^ (P V ¬Q) ^ ¬(P ^ S)} c) C = [¬P → (P → Q)] → [Q → (P → P)] d) X = [(PV¬Q) A(QV¬S) ASA¬(PAQ AS)]

7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P ^ Q)] ^ [P ^ (P ^ Q)]} b) B = {[¬(P ^ S)V ¬Q] ^ (P V ¬Q) ^ ¬(P ^ S)} c) C = [¬P → (P → Q)] → [Q → (P → P)] d) X = [(PV¬Q) A(QV¬S) ASA¬(PAQ AS)]

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.CT: Test

Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...

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Question

7. Simplify the following using the algebra of propositions. Show your solutions.
a) A =
{[QV (P ^ Q)] ^ [P ^ (P ^ Q)]}
b) B = {[¬(P ^ S)V ¬Q] ^ (P V ¬Q) ^ ¬(P ^ S)}
c) C = [¬P → (P → Q)] → [Q → (P → P)]
d) X = [(PV¬Q) A(QV¬S) ASA¬(PAQ AS)]

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