In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How m

English

Gujarati

Hindi

1.Set Theory

easy

In a committee, $50$ people speak French, $20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

A

$60$

B

$60$

C

$60$

D

$60$

Solution

Let $F$ be the set of people in the committee who speak French, and $S$ be the set of people in the committee who speak Spanish

$\therefore n(F)=50, n(S)=20, n(S \cap F)=10$

We know that:

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

$=20+50-10$

$=70-10=60$

Thus, $60$ people in the committee speak at least one of the two languages.

Standard 11

Mathematics

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