Question

X intersection of sets x minus y

Answer 1

The intersection of sets X and (X - Y) is equal to the set X minus Y.

or

X ∩ (X - Y) = X - Y

Explanation:

The intersection of sets X and (X - Y) can be written as:

X ∩ (X - Y)

We know that (X - Y) represents the set of elements that are in X but not in Y. Therefore, the elements in the intersection of X and (X - Y) must be in both sets.

Let's say a particular element x is in both sets. This means that x is in X and x is in (X - Y). But if x is in (X - Y), then it is in X but not in Y. So, x is in X and not in Y. This implies that x is in the set X intersect Y, since it is in X and it is also in the set of elements that are in both X and Y.

Therefore, we can conclude that:

X ∩ (X - Y) = X - Y

Answer 2

Explanation:

Assuming that "X" refers to a set and "x" and "y" refer to elements of sets, the expression "X intersection of sets x minus y" is not well-formed.

To take the intersection of sets, we need to have two or more sets. So, if we assume that "x" and "y" are themselves sets, we could write the expression as follows:

X ∩ (x \ y)

In this expression, "∩" is the intersection operator, and "" is the set difference operator. So "x \ y" is the set of elements in "x" that are not in "y", and the intersection of that set with "X" gives us the elements that are in both "X" and "x", but not in "y".

For example, if we had:

X = {1, 2, 3, 4}

x = {2, 3, 5, 6}

y = {3, 4, 6, 7}

Then:

x \ y = {2, 5}

X ∩ (x \ y) = {2}