Question

If S is the set of positive integers that are multiples of 7, and if T is the set of positive integers that are multiple of 13, how many integers are in the intersection of S and T?

(A) None

(B) One

(C) Seven

(D) Thirteen

(E) More than thirteen

Answer 1

E. More than thirteen

Step-by-step explanation:

S is the set of multiples of 7, meaning 7, 14, 21, 28 and so on to infinity

T is the same but with 13 instead

Both sets are infinite.

The first intersection would be 7x13 (91)

Though it would be difficult to find 14 of them to prove it, we don't have to since we know both sets are infinite and will eventually have intersections the higher they go

Answer 2

`\huge\boxed{\sf E. \ More \ than \ thirteen}`

Step-by-step explanation:

S is a set of multiples of 7.

T is a set of multiples of 13.

So, The first element in the set would be 7*13 = 91.

Likewise, The set of intersection of 9 and 13 would include all of the multiples of 91. This means the it consists of infinite number of elements.

Hence, Integers in intersection set will be more than 13.

`\rule[225]{225}{2}`

Hope this helped!

~AH1807