Question

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In a college there are 25 teachers who teach engineering or management. Of these, 15 teach engineering and 6 teach both engineering and management. How many teach management.
[Answer is 16 ]​

Answer 1

Answer:

Number of Teachers who teach management = 16

Step-by-step explanation:

Teachers who teach Engineering =n(E) = 15

Let Teachers who teach management =n(M)

Number of teachers who teach

engineering Or management =n(EUM) = 25,

Number of teachers who teach

engineering and management = n(EnM) =6.

We know that,

n(E)+n(M)-n(EnM)=n(EUM)

=> 15+n(M)-6=25

=> 9+n(M) = 25

=> n(M) = 25-9

=> n(M)=16

Therefore,

Teachers who teach management =n(M) = 16

•••♪

Answer 2

Explanation:-

Number of teachers who teach engineering or management = 25

• As we know or means union.

n( E ∪ M) = 25

Number of Teachers who teach engineering is = 15

n ( E ) = 15

Number of teachers who teach both engineering and management = 6

n( E ∩ M) = 6

• As both means intersection.

To find :-

Number of teachers teaches management.

Solution:-

By using operations of sets.

n ( E ∪ M) = n( E) + n( M) - n ( E∩M)

• Put the above values,

→ 25 = 15 + n( M) - 6

→ 25 = 9 + n( M)

→ 25 - 9 = n( M)

→ n( M ) = 16

hence,

The number of teacher who teaches management is 16.