If $X$ and $Y$ are two sets such that $n(X) = 17$, $n(Y) = 23$ and $n(X \cup Y) = 38$, find $n(X \cap Y)$.

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Accepted Answer

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> [!TLDR]
> Using $n(X\cup Y) = n(X)+n(Y)-n(X\cap Y)$, we get $n(X\cap Y) = 2$.
>
> For any two sets $X$ and $Y$:
> $$n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)$$
>
> Rearranging for $n(X \cap Y)$:
> $$n(X \cap Y) = n(X) + n(Y) - n(X \cup Y)$$
> …

Q.If $X$ and $Y$ are two sets such that $n(X) = 17$ , $n(Y) = 23$ and $n(X \cup Y) = 38$ , find $n(X \cap Y)$ .

Concept understanding — Practical Problems on Union and Intersection of Two Sets

Q.If XXX and YYY are two sets such that n(X)=17n(X) = 17n(X)=17, n(Y)=23n(Y) = 23n(Y)=23 and n(X∪Y)=38n(X \cup Y) = 38n(X∪Y)=38, find n(X∩Y)n(X \cap Y)n(X∩Y).

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Q.If $X$ and $Y$ are two sets such that $n(X) = 17$ , $n(Y) = 23$ and $n(X \cup Y) = 38$ , find $n(X \cap Y)$ .

Unlock everything free for 14 days