Answer to Question #269491 in Discrete Mathematics for Anonymous

Question

Q1: Let A, B, C be three sets. Prove that (𝐴 − 𝐵) − 𝐶 = (𝐴 − 𝐶) − (𝐵 − 𝐶) using following proof methods:

a) Membership table

b) Set builder notation and propositional logic

Q2 : Find generalized union and intersection as defined below for each of the following collections of sets

⋃ 𝐴𝑖

∝

1 and ⋂ 𝐴𝑖

∞

1

a) 𝐴𝑖 = {𝑖, 𝑖 + 1,𝑖 + 2, … }

b) 𝐴𝑖 = {0,𝑖}

c) 𝐴𝑖 = {−𝑖, − 𝑖 + 1, … , −1, 0, 1, … , 𝑖 − 1, 𝑖}

d) 𝐴𝑖 = {−𝑖, 𝑖}