Algebra question

Question

Let A = {1, 3, 5, 7}, B = {5, 6, 7, 8}, C = {5, 8}, D = {2, 5, 8}, and U = {1, 2, 3, 4, 5, 6, 7, 8}. Decide if the set relationship is true or false.

C ⊆ D

Answer 1

The object is to determine if C is a subset of D. This requires every member of set C to also be a member of set D.

Since both 2 and 5 are also members of set D, set C is a subset of D.

Answer 2

Let's take a look at the set relationship in question:

C ⊆ D

Since C and D are the only sets mentioned in this relationship, let's take a look at set C and set D

C = {5, 8}

D = {2, 5, 8}

So C is a set that only has 5 and 8, while D is a set that has 2 as well as 5 and 8. All of the elements that can be found in C can also be found in D, so the set relationship C ⊆ D is true.

I hope that helps and makes sense!