Q. 34.4( 5 Votes )
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.
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