Question

In building with 20 families it was found that 15 families having members voted for bjp and 8 families having members voted for congress if 2 families having members voted for none how many families voted for bjo and congress

Answer 1

$\sf{\underline{Given:}}$

Total no. of families $\sf{= 20}$

No. of families do not vote $\sf{= 2}$

No. of families voting BJP $\sf{= 15}$

$\sf{\underline{Note:}}$ Let X $\sf{= 15}$

No. of families voting BJP congress $\sf{= 8}$

$\sf{\underline{Note:}}$ Let Y $\sf{= 8}$

$\sf{\underline{So:}}$

Total no. of families,

Who had members to vote

$\implies$ $\sf{20- 2}$

$\implies$ $\sf{18}$

$\implies$ $\sf{n(X \cup Y)}$

$\sf{\underline{We\:know\:that:}}$

$\boxed{\sf{n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)}}$

$\sf{n(X \cap Y) = n(X) + n(Y) - n(X \cup Y)}$

$\implies$ $\sf{15 + 8 - 18}$

$\implies$ $\sf{15 - 10}$

$\implies$ $\boxed{\huge{\sf{5}}}$

$\sf{\underline{So:}}$

There are 5 families who had members to vote both BJP and Congress.