Question

B= {x:x= n/ 2n+1, n€N and n>5​

Answer 1

Answer

2n+1

2×1+1=3

2×2+1=5

2×3+1=7

2×4+1=9

Roster from= {3,5,7,9,...}

Answer 2

= All the natural numbers i.e. {1, 2, 3…..} B = All the even natural numbers i.e. {2, 4, 6, 8…} C = All the odd natural numbers i.e. {1, 3, 5, 7……} D = All the prime natural numbers i.e. {1, 2, 3, 5, 7, 11, …} (i) A ∩ B Here, A contains all elements of B. ∴ B ⊂ A = {2, 4, 6, 8…} ∴ A ∩ B = B (ii) A ∩ C Here, A contains all elements of C. ∴ C ⊂ A = {1, 3, 5…} ∴ A ∩ C = C (iii) A ∩ D Here, A contains all elements of D. ∴ D ⊂ A = {2, 3, 5, 7..} ∴ A ∩ D = D (iv) B ∩ C B ∩ C = ϕ Since, there is no natural number which is both even and odd at same time. (v) B ∩ D B ∩ D = 2 Since, {2} is the only natural number which is even and a prime number. (vi) C ∩ D C ∩ D = {1, 3, 5, 7…} = D – {2} Hence, every prime number is odd except {2}.Read more on Sarthaks.com - https://www.sarthaks.com/650620/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