(C) Let $M$ denote the set of teachers who teach mathematics and $P$ denote the set of teachers who teach physics. From the problem,we have: $n(M \cup

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(C) Let $M$ denote the set of teachers who teach mathematics and $P$ denote the set of teachers who teach physics. From the problem,we have: $n(M \cup P) = 20$ $n(M) = 12$ $n(M \cap P) = 4$ We use the formula: $n(M \cup P) = n(M) + n(P) - n(M \cap P)$ Substituting the values: $20 = 12 + n(P) - 4$ $20 = 8 + n(P)$ $n(P) = 20 - 8$ $n(P) = 12$ Thus,$12$ teachers teach physics.

Class 11 Mathematics Set Theory Word Problem - Set Theory

Easy

In a school,there are $20$ teachers who teach mathematics or physics. Of these,$12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics?

A
$8$
B
$10$
C
$12$
D
$16$

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Set Theory

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Word Problem - Set Theory

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

MediumJEE MAIN 2022

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The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

EasyAP EAMCET 2021

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The probability of failing in Physics is $20\%$,and the probability of failing in Mathematics is $10\%$. What is the probability of failing in at least one subject (in $\%$)?

Medium

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Let $A$ be a set containing $n$ elements. If $P$ and $Q$ are two subsets of $A$, then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \phi$ is:

EasyWBJEE 2022

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In a group of $400$ people,$250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

Easy

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In a school,there are $20$ teachers who teach mathematics or physics. Of these,$12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics?

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