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If a set B has n elements, then what is the total number of subsets of B.
1. If a set B has n elements, then what is the total number of subsets of B. Justify your answer.
Solution: If a set B has “n” elements, then the total number of subsets of B is 2n.
For example, if B contains 5 elements, say B = {1, 2, 3, 4, 5}, then the total number of subsets of B is 25 = 32.
2. If X and y are the two finite sets, such that n(X U Y) = 36, n(X) = 20, n(Y) = 28, then find n( X ∩ Y).
Solution: n(X) = 20, n (Y) = 28, n (X U Y) = 36.
As we that, n(X U Y) = n(X) + n(Y) – n(X ∩ Y)
On rearranging the above formula, we get;
n(X ∩ Y) = n(X) + n(Y) – n(X U Y)
Now, substitute the given values in the above formula, we get;
n(X ∩ Y) = 20 + 28 – 36
n(X ∩ Y) = 48 – 36
n(X ∩ Y) = 12.
Hence, n(X ∩ Y) is 12.
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