Question

If set D is not the empty set but is a subset of set E, then which of the following is true?

D ∩ E = D
D ∩ E = E
D ∩ E = ∅

Answer 1

D∩E=D This is because since D is a subset of E then the elements they will have in common are the elements in D and D is not a null set

Answer 2

Answer: The correct option is (A) D ∩ E = D.

Step-by-step explanation: Given that a set D is not the empty set but is a subset of set E.

We are to select the TRUE statement.

SUBSET : A set A is said to be a subset of another set B if every element of set A is also in set B.

Since the set D is the subset of set E, so all the elements of set D will also be in set E.

So, the intersection of the sets D and E will be the set D.

That is, D ∩ E = D.

For example, let D = {1, 2, 3} and E = {0, 1, 2, 3, 4, 5}.

Then, D is a subset of E and D ∩ E = {1, 2, 3} = D.

Thus, option (A) is CORRECT.