Answer to Question #302625 in Discrete Mathematics for Azizi

Question

There is a set X = {1, 2, 3, 4, 5}. Find the sets A, B, C such that A ⊆ X, B ⊆ X,

C ⊆ X,

(A ∪ B) ⊆ (A ∩ C)

and C 6⊆ B.

Answer 1

X = {1, 2, 3, 4, 5}

A ⊆ X, B ⊆ X,

C ⊆ X,

(A ∪ B) ⊆ (A ∩ C)

and C ⊄ B.

A = {2, 3}                     and                 B = {3}            Therefore,      A ∪ B = {2, 3}

A = {2, 3}                     and                 C = {1, 2, 3}     Therefore,      A ∩ C = {2, 3}

(A ∪ B) ⊆ (A ∩ C)     =          (2, 3) ⊆ (2, 3), and

C ⊄ B                 = (1, 2, 3) ⊄ (3)

Therefore,      A = {2, 3},      B = {3}, and   C = {1, 2, 3}