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

∴ A ∩ B = B

ii. A ∩ C

A contains all elements of C.

∴ C ⊂ A

∴ A ∩ C = C

iii. A ∩ D

A contains all elements of D.

∴ D ⊂ A

∴ 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…}

Every prime number is odd except 2.