Question

Suppose that a = 2, 4, 6, b = 2, 6, c = 4, 6, and d = 4, 6, 8. Determine which of these sets are subsets of which other sets?

Answer 1

Set b is a subset of set a and d, and set c is a subset of set d. There are no other subset relationships among the given sets.

Step-by-step explanation:

To determine which of the sets given are subsets of others, let's consider each set individually. The sets are a = {2, 4, 6}, b = {2, 6}, c = {4, 6}, and d = {4, 6, 8}. A set X is considered a subset of another set Y if every element in X is also in Y.

• Set b is a subset of set a because all elements of b (which are 2 and 6) are also in a.
• Set c is not a subset of a because it contains the element 4 which is not in a.
• Set c is a subset of d because all elements of c are also in d.
• Neither set a nor b is a subset of d because they both lack the element 8 which is in d.
• Set b can also be considered a subset of d as it only contains elements that are in d.

In conclusion, b is a subset of a and d, and c is a subset of d, but no other subset relationships exist between these sets.