If n(X) = 40, n(Y) = 60 and n(X $\rm \cup$ Y) = 85, then find n(X $\rm \cap$ Y) and no(Y) by using f

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Asked by Atith Adhikari · 1 year ago

If n(X) = 40, n(Y) = 60 and n(X $\rm \cup$ Y) = 85, then find n(X $\rm \cap$ Y) and n_o(Y) by using formula.

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Solution

Given

$\rm n(X) = 40, n(Y) = 60, n(X \cup Y) = 85$

By using the formula for the union of two sets, we get

$\rm n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)$

$\rm or, n(X \cap Y) = n(X) + n(Y) - n(X \cup Y)$

$\rm or, n(X \cap Y) = 40 + 60 - 85$

$\rm \therefore n(X \cap Y) = 15$

Now, we show the above information in a Venn diagram.