find (i) A ∩ B (ii) A ∩ C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D

If A = {x: x is a natural number}, B ={x: x is an even natural number}
C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(i) A ∩ B
(ii) A ∩ C
(iii) A ∩ D
(iv) B ∩ C
(v) B ∩ D
(vi) C ∩ D
Answer
Natural numbers are 1, 2, 3, 4, 5 …
Even natural numbers are 2, 4, 6, 8 …
Odd natural numbers are 1, 3, 5, 7, 9 …
Prime numbers are 2, 3, 5, 7 …
(i) A ∩B ={1, 2, 3, 4, 5 … } ∩ {2, 4, 6, 8 … } = {2, 4, 6, 8 … } = B
(ii) A ∩ C = {1, 2, 3, 4, 5 … } ∩ {1, 3, 5, 7, 9 …} = {1, 3, 5, 7, 9 …} = C
(iii) A ∩ D = {1, 2, 3, 4, 5 … } ∩ {2, 3, 5, 7 … } = {2, 3, 5, 7 … } = D
(iv) B ∩ C = {2, 4, 6, 8 … } ∩ {1, 3, 5, 7, 9 …} = Φ
(v) B ∩ D ={2, 4, 6, 8 … } ∩ {2, 3, 5, 7 … } = {2}
(vi) C ∩ D ={1, 3, 5, 7, 9 …} ∩ {2, 3, 5, 7 … } = { 3, 5, 7 ,11 … } = D – {2} Or { x : x is an odd prime number }