Question

Q22. A and B are two sets such that n(A-B)=14+x; n(B-A)=3x and n(A  B)=x. Draw a diagram to illustrate this information. If n(A)=n(B). Find (i) the value of x. (ii) n(A U B).

Answer 1

Evening Here is your answer:-)

n(a-b)=20+x

n(b-a)=3x

n(a ∩ b) =x+1

We know that

n(a-b) = n(a)-n(a ∩ b)

∴n(a) = n(a-b) + n(a ∩ b)

= (20+x) + (x + 1)

= 2x + 21

Similarly, n(b) = n(b-a) + n(a ∩ b)

=3x + (x+1)

=4x + 1

According to the question,

n(a) = n(b)

∴2x + 21 = 4x +1

⇒2x = 20

∴ x = 10

If any doubt ask it in comment box.✌

Answer 2

Answer:

Hey mate, here's your answer;

n(A-B) = 14+x

n(B-A) = 3x

n(A∩B) = x

we know that:

n(A) = n(A-B) + n(A∩B)

⇒ n(A) = 14+x+x = 14+2x                                        ( 1 )

Similarly,

n(B) = n(B-A) + n(A∩B)

⇒ n(B) = 3x+x = 4x                                                  ( 2 )

It is given that,

n(A) = n(B)

So, ( 1 ) =  ( 2 )

⇒ 14+2x = 4x

∴ x = 7