Question

Let A = {1, 2, 3, 4}, B = {2, 4, 6}. Then the number of sets C such that A ∩ B ⊆ C ⊆ A ⋃ B is

A) 6
B) 9
C) 8
D) 10

Answer 1

The number of sets C such that A ∩ B ⊆ C ⊆ A ⋃ B is 3.

Step-by-step explanation:

To find the number of sets C such that A ∩ B ⊆ C ⊆ A ⋃ B, we need to determine the possible subsets of A ∪ B that contain A ∩ B.

Since A = {1, 2, 3, 4} and B = {2, 4, 6}, A ∩ B = {2, 4}.

Now, we can find the possible subsets of A ∪ B that contain {2, 4} which are {2, 4}, {2, 4, 6}, and {1, 2, 3, 4, 6}. Therefore, the number of sets C is 3.