Question 15 We want to prove that for all A, B, C ≤ U, (AUC) - (CB) = (A − C) u [(A − B) u (C − B)] is an identity. Consider the following incomplete proof: ZE (AUC) - (CB) iff (z = A or z = C) and (z # (CB)) iff (z € A or z = C) and (z # C or z # B) Step 4 iff [(z € A or z = C) and (z = C')] or [(z = A or z = C) and (Z = E Step 6 B')] iff [(z = A and z = C')] or [(z = A and z = B') or (z = C and z = B')] iff [(z = A - C)] or [(z = (A − B) or (z = C – B)] iff ZE (AC) U [(A - B) (C-B)]
Question 15 We want to prove that for all A, B, C ≤ U, (AUC) - (CB) = (A − C) u [(A − B) u (C − B)] is an identity. Consider the following incomplete proof: ZE (AUC) - (CB) iff (z = A or z = C) and (z # (CB)) iff (z € A or z = C) and (z # C or z # B) Step 4 iff [(z € A or z = C) and (z = C')] or [(z = A or z = C) and (Z = E Step 6 B')] iff [(z = A and z = C')] or [(z = A and z = B') or (z = C and z = B')] iff [(z = A - C)] or [(z = (A − B) or (z = C – B)] iff ZE (AC) U [(A - B) (C-B)]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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QUESTION 15
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