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integers divisible by 2.

Suppose A = {2,4,6,8,10} and B={1,2,3,4,5,6,7,8,9,10}.

The intersection between them is exactly A.

A ∩ B means A (intersection) B, i.e common values in both the sets A and B

Here it means all integers divisible by 2,

i.e the common of A and B is to be taken to A ∩ B

A = {... -6, -4, -2, 0, 2, 4, 6....}

B = {... -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6....}

then A ∩ B =(... -6, -4, -2, 0, 2, 4, 6....)

i.e A ∩ B = A

A Note :

Union and Intersection :

The UNION of two sets is the set of elements which are in either set.

For example:

Let A = {1,2,3} and B = {3,4,5}

Now the UNION of A and B, written A U B = {1,2,3,4,5}

There is no need to list the 3 twice.

The INTERSECTION of two sets is the set of elements which are in both sets.

For example:

Let A = {1,2,3} and B = {3,4,5}

The INTERSECTION of A and B, written A ∩ B = {3}

.

A ∩ B = A

In particular, if X and Y are sets, and X is a subset of Y, we have that X ∩ Y = X

Proof:

(1) X ∩ Y is a subset of X.

Take q in X ∩ Y. Then q is in X and Y. So q is in X.

(2) X is a subset of X ∩ Y.

Take q in X. Then q is in Y too since X is a subset of Y. Thus, since q is in X and Y, q is in X ∩ Y

Since X ∩ Y is a subset of X, and X is a subset of X ∩ Y, we have that X = X ∩ Y.

Those are called variables