Question

7. Let B(k)={k, k+1,k+2,……}, where k=1,2,3,…..
a. Find B(1)∩B(2)∩……∩B(1000).
b. Find minimum number into B(1)∩B(2)∩……∩B(1005) divisible by 11.

Answer 1

B(k) = {k, k+1, k+2, ..... }

where k=1,2,3,....

a)

B(1) = { 1,2,3,.... }

B(2) = { 2,3,4,.... }

.

.

.

B(1000) = { 1000, 1001, 1002,.... }

B(1) . B(2) . B(3). ..... .B(1000) = {1000, 1001, .....}

b)1012