State True or False.
In a committee $50$ people speak French, $20$ speak Spanish, and $10$ speak both Spanish and French. The number of persons speaking at least one of these two languages is $60$ .

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Solution

The correct option is A: $60$
$n (S) =$ No. of people speak Spanish $= 20$
$n (F) =$ No. of people speak French $= 50$
$n (S \cap F) =$ No. of people speak Spanish and French both $= 10$
$n (S \cup F) =$ No. of people speak at least one of these two languages
We know that,
$n (S \cup F)$ = $n (S) + n (F) - n (S \cap F)$

$\Rightarrow n (S \cup F) = 20 + 50 - 10 = 60$

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State True or False. In a committee 50 people speak French, 20 speak Spanish, and 10 speak both Spanish and French. The number of persons speaking at least one of these two languages is 60.

The correct option is A: 60n(S)= No. of people speak Spanish =20n(F)= No. of people speak French =50n(S∩F)= No. of people speak Spanish and French both =10n(S∪F)= No. of people speak at least one of these two languages We know that, n(S∪F) = n(S)+n(F)−n(S∩F) ⇒n(S∪F)=20+50−10=60

State True or False.
In a committee $50$ people speak French, $20$ speak Spanish, and $10$ speak both Spanish and French. The number of persons speaking at least one of these two languages is $60$ .