Venn diagram

next question: find the smallest integer n such that 840n is a perfect square

Hi,

It is useful to list the members of each set, i.e.

E (i.e. the universal set) = {1, 2, 3, ..., 8}, A = {1, 2, 3, 4, 5}, B = {2, 3, 4}.

Then n(A union B) refers to the number of elements in the union of A and B,

and n(A intersect B)' refers to the number of elements in the complement of A intersect B (i.e. those elements that lie outside of the intersection).

Thanks!

Cheers,
Wen Shih

next question: find the smallest integer n such that 840n is a perfect square

Hi,

First, express 840 as a product of prime factors, i.e. (2^3)(5)(21).

Next, we must consider two facts:

1. Any perfect square must have powers which are divisible by 2.

2. 840n must have prime factors 2, 5 and 21.

Try it, thanks!

Cheers,
Wen Shih

Hi,

First, express 840 as a product of prime factors, i.e. (2^3)(5)(21).

Next, we must consider two facts:

1. Any perfect square must have powers which are divisible by 2.

2. 840n must have prime factors 2, 5 and 21.

Try it, thanks!

Cheers,
Wen Shih

Hi wen shih, 21 is not a prime factor ah......

so the accurate solution should be (2^3)(3)(5)(7) for 840 prime factors, and thus n= (2)(3)(5)(7)

Hi,

Thanks for pointing out my error :)

Cheers,
Wen Shih

welcome. :)