In a school there are $20$ teachers who teach mathematics or physics. Of these $12$ teach mathematics and $4$ teach both mathematics and physics. The number of teachers who teach only physics are

4

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12

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8

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16

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Solution

The correct option is A $8$
$M =$ Mathematics
$P =$ Physics
$m (M \cup P) = 20, n (M) = 12, n (M \cap P) = 4$
Fact $m (M \cup P)$
$= n (M) + n (P) - n (M \cap P) \Rightarrow n (P) = n (M \cup P) - n (M) + n (M \cap P) = 20 - 12 + 4 = 12$
$n$ (only Physics) $= n (P) - n (M \cup P) = 12 - 4 = 8$

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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 mathematics and physics. The number of teachers who teach only physics are

The correct option is A 8M= MathematicsP= Physicsm(M∪P)=20,n(M)=12,n(M∩P)=4Fact m(M∪P)=n(M)+n(P)−n(M∩P)⇒n(P)=n(M∪P)−n(M)+n(M∩P)=20−12+4=12n (only Physics)=n(P)−n(M∪P)=12−4=8

In a school there are $20$ teachers who teach mathematics or physics. Of these $12$ teach mathematics and $4$ teach both mathematics and physics. The number of teachers who teach only physics are

The correct option is A $8$
$M =$ Mathematics
$P =$ Physics
$m (M \cup P) = 20, n (M) = 12, n (M \cap P) = 4$
Fact $m (M \cup P)$
$= n (M) + n (P) - n (M \cap P) \Rightarrow n (P) = n (M \cup P) - n (M) + n (M \cap P) = 20 - 12 + 4 = 12$
$n$ (only Physics) $= n (P) - n (M \cup P) = 12 - 4 = 8$