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 intersect E=D (the first one you have)

Explanation:

D is a subset of E

That means all the elements in D are also in E

So the intersection of D and E is D.

The first thing you wrote is correct, that is, D intersect E=D is right

Answer 2

`D\cap E`=D

Explanation:

We are given that D is not empty set but D is a subset of set E.

We have to find the true statement.

`D\\eq \phi`

D is a subset of set E

Therefore,
`D\subset E\\eq \phi`

Intersection: It is the set of common elements of two sets.

Therefore,
`D\cap E`=D

Because E contains all elements of D .

Hence, Option A is true.