Question

if X and Y are two sets such that X union Y has 18 elements,X has 8 elements and Y has 15 elements,how manu elements does X intersection Y have?​

Answer 1

Answer:

5

Step-by-step explanation:

E(XY) = E(X) + E(Y) - E(X+Y)

E(XY) = 15 + 8 - 18 = 5

You can also simply thing that when you directly add both sets which elements was common counted twice . And in union they are in once . So subtract both

Answer 2

n(X ⋂ Y) = 5

Given:

n(X) = 8

n(X U Y) = 18

n(Y) = 15

To Find:

n(X ⋂ Y)

Calculating:

The formula used to find the union of sets is:

n(X U Y) = n(X) + n(Y) - n(X ⋂ Y)

Taking n(X ⋂ Y) to the other side of the formula we get:

n(X ⋂ Y) = n(X)  + n(Y) - n(X U Y)

Substituting all the values that are known to us in this formula we get:

n(X ⋂ Y) = 8 + 15 - 18

n(X ⋂ Y) = 23 - 18

n(X ⋂ Y) = 5

Therefore, n(X ⋂ Y) = 5.