Consider the sets below. A = {x|x is a polygon}, B = {x|x is a triangle}. Which is true?
A ⊂ B, A ⊃ B, A ⊆ B, A ⊇ B

Solution:

Since a triangle is a polygon with three sides it implies that it is a proper subset of polygons.

Therefore it can be stated that A ⊃ B.

A ⊃ B means that B is a proper subset of A.

Proper subset means that A definitely has necessarily more elements than the number of elements of B.

In other words A always and necessarily contains B in it. In the present example A is a set which contains polygons and hence comprises various n sided polygons.

The set B comprises only triangles, hence set A not only has all the elements of set B but also beyond that.

Therefore A has definitely more elements than set B. The symbol of proper subset is ⊃ or ⊂.

A ⊂ B implies that A is a proper subset of B whereas A ⊃ B means that B is a proper subset of A.

For the given problem statement the correct option is: A ⊃ B

The symbol ⊆ means subset of. The difference between subset and proper set is that the two sets may have an equal number of elements.

If A ⊆ B, it implies that A is a subset of B which means that B contains A, but may also sometimes have the same number of elements as A.

Let us take an example:

Suppose we have A = {x|x is a triangle}, B = {x|x is an equilateral triangle}

In this case it is possible that the number of elements of A and B be same though generally speaking A contains B because A comprises all kinds of triangles.

But it may happen that A might have equilateral triangles and that too same number as set B. So for such cases it is stated that B ⊆ A.

Therefore, the correct set for the given relations A = {x|x is a polygon}, B = {x|x is a triangle} is A ⊃ B

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Consider the sets below. A = {x|x is a polygon}, B = {x|x is a triangle}. Which is true?

Summary:

The correct set for the given relations A = {x|x is a polygon}, B = {x|x is a triangle} is A ⊃ B.