If S and T are two sets such that S has 21 elements, T has 32 elements, and S cap ,T has 11 elements

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1.Set Theory

easy

If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?

A

$42$

B

$42$

C

$42$

D

$42$

Solution

It is given that:

$n(S)=21, n(T)=32, n(S \cap T)=11$

We know that:

$n(S \cup T)=n(S)+n(T)-n(S \cap T)$

$\therefore n(S \cup T)=21+32-11=42$

Thus, the set $(S \cup T)$ has $42$ elements.

Standard 11

Mathematics

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