Practice Plus a. Let A = 536, B = 51, 26, C = 52, 46, and U = 51, 2, 3, 4, 5, 66. Find

Chapter 2, Problem 70

(choose chapter or problem)

a. Let A = {3}, B = {1, 2}, C = {2, 4}, and U = {1, 2, 3, 4, 5, 6}. Find \((A \cup B)^{\prime} \cap C\) and \(A^{\prime} \cap\left(B^{\prime} \cap C\right)\).

b. Let A = {d, f, g, h}, B = {a, c, f, h}, C = {c, e, g, h}, and \(U=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \ldots, \mathrm{h}\}\). Find \((A \cup B)^{\prime} \cap C\) and \(A^{\prime} \cap\left(B^{\prime} \cap C\right)\).

c. Based on your results in parts (a) and (b), use inductive reasoning to write a conjecture that relates \((A \cup B)^{\prime} \cap C\) and \(A^{\prime} \cap\left(B^{\prime} \cap C\right)\).

d. Use deductive reasoning to determine whether your conjecture in part (c) is a theorem.

Text Transcription:

(A cup B)^prime cap C

A^prime cap(B^prime cap C)

U={mathrm a, mathrm b, mathrm c, ldots, mathrm h}

(A cup B)^prime cap C

A^prime cap(B^prime cap C)

(A cup B)^prime cap C

A^prime cap(B^prime cap C)