Let A = {x:x ∈ N}, B = {x:x = 2n, n ∈ N), C = {x:x = 2n – 1, n �

1.	Let A = {x:x ∈ N}, B = {x:x = 2n, n ∈ N), C = {x:x = 2n – 1, n ∈ N} and, D = {x:x is a prime natural number} Find: i. A ∩ B ii. A ∩ C iii. A ∩ D iv. B ∩ C v. B ∩ D vi. C ∩ D
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 ∴ 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

Let A = {x:x ∈ N}, B = {x:x = 2n, n ∈ N), C = {x:x = 2n – 1, n ∈ N} and, D = {x:x is a prime natural number} Find: i. A ∩ B ii. A ∩ C iii. A ∩ D iv. B ∩ C v. B ∩ D vi. C ∩ D

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

∴ 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