Question

Q1. If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ∩ Y have?


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Answer 1

Answer:

N(xΠY) = N(X) + N(Y) - N(XUY)

N(XΠY) = 28 + 32 -50

N(XΠY) = 10.

Answer 2

Given:

n(X∪Y)=50

n(X)=28

n(Y)=32

To find:

The number of elements in X ∩ Y

Solution:

The required elements in X ∩ Y are 10.

We can calculate the required number by adding the elements of X and Y and deducting the elements present in their union.

So, n(XUY)=n(X)+n(Y)- n(X∩Y) (1)

The sum of X and Y's elements=n(X)+n(Y)

Using values,

=28+32

=60 elements

Now, we will put the values in (1),

50=60-n(X∩Y)

n(X∩Y)=60-50

On subtracting,

n(X∩Y)=10

Therefore, the required elements in X ∩ Y are 10.