Let A and B be two sets such that: n (A) = 20, n (A ∪ B) = 42 and

1.	Let A and B be two sets such that: n (A) = 20, n (A ∪ B) = 42 and n (A ∩ B) = 4. Find(i) n (B)(ii) n (A – B)(iii) n (B – A)
Answer» (i) n (B) As we know, n (A ∪ B) = n (A) + n (B) – n (A ∩ B) By substituting the values we get 42 = 20 + n (B) – 4 42 = 16 + n (B) n (B) = 26 ∴ n (B) = 26 (ii) n (A – B) As we know, n (A – B) = n (A ∪ B) – n (B) By substituting the values we get n (A – B) = 42 – 26 = 16 ∴ n (A – B) = 16 (iii) n (B – A) As we know, n (B – A) = n (B) – n (A ∩ B) By substituting the values we get n (B – A) = 26 – 4 = 22 ∴ n (B – A) = 22

Let A and B be two sets such that: n (A) = 20, n (A ∪ B) = 42 and n (A ∩ B) = 4. Find(i) n (B)(ii) n (A – B)(iii) n (B – A)

Answer»

(i) n (B)

As we know,

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

By substituting the values we get

42 = 20 + n (B) – 4

42 = 16 + n (B)

n (B) = 26

∴ n (B) = 26

(ii) n (A – B)

As we know,

n (A – B) = n (A ∪ B) – n (B)

By substituting the values we get

n (A – B) = 42 – 26

= 16

∴ n (A – B) = 16

(iii) n (B – A)

As we know,

n (B – A) = n (B) – n (A ∩ B)

By substituting the values we get

n (B – A) = 26 – 4

= 22

∴ n (B – A) = 22