Question -
Answer -
A = All natural numbers i.e. {1, 2, 3…..}
B = All even natural numbers i.e. {2, 4, 6, 8…}
C = All odd natural numbers i.e. {1, 3, 5, 7……}
D = All prime natural numbers i.e. {1, 2, 3, 5, 7, 11, …}
(i) A ∩ B
A contains all elements of B.
∴ B ⊂ A = {2, 4, 6, 8…}
∴ A ∩ B = B
(ii) A ∩ C
A contains all elements of C.
∴ C ⊂ A = {1, 3, 5…}
∴ A ∩ C = C
(iii) A ∩ D
A contains all elements of D.
∴ D ⊂ A = {2, 3, 5, 7..}
∴ A ∩ D = D
(iv) B ∩ C
B ∩ C = ϕ
There is no natural number which is both even and odd at same time.
(v) B ∩ D
B ∩ D = 2
{2} is the only natural number which is even and a prime number.
(vi) C ∩ D
C ∩ D = {1, 3, 5, 7…}
= D – {2}
Every prime number is odd except {2}.