Question

Let A = {a1, a2, a3 ......... an} be a set of ‘n’
distinct natural number and n greater than or equal to 8. Which of
the following will always be a natural number :
(A) a1 + a2 + a3 -– a7 (B) (a1-– a5)5
(C) an- a1 (D) (a1-an)8

Answer 1

There's no way of knowing, we can't tell which terms are greater than others, to know which we can subtract from which and still get a positive result.

Answer 2

But, see, if a1-an is a negative number, then (a1-an)^8 is always +ive, believe. Sorry for inconvenience, the option (b) is (a1-a5)^5 and (d) is (a1-an)^8.

Answer 3

Ah, ok. I though it was times 5 in B and times 8 in D. Then of course D is the option.

Answer 4

the exponent indicator helps out alot ;)

Answer 5

So that means (d) is the best bet. Thanks a lot. I have few other questions.

Answer 6

Bring them.