Question

Let A={3,4,5} and B={4,5,6} and let S be the divides relation. That is for all (x,y) is an element of A x B
x S y <---> x|y
State explicitly which ordered pairs are in S and s^-1

Answer 1

Which numbers in the set A divide which numbers in the set B?

Answer 2

well I am getting confused when divided does it have to be an integer?

Answer 3

Correct. We say that \(a|b\) if \(b=a\,k\) for some integer \(k\).

Answer 4

ohh ok so 4/4 and 5/5 and what about 3/6

Answer 5

\(6=3\cdot2\) so 3 divides 6.

Answer 6

So what are the three pairs in S?

Answer 7

(4,4) (5,5) (3,6)

Answer 8

uh oh being paged ill brb in a sec

Answer 9

back what abt its inverse?

Answer 10

does it include (6,3)?

Answer 11

Remind me what does the question mean by S^(-1)?

Answer 12

like its inverse
so if S={(1,2)(3,4)}
then its inverse wld equal s^(-1)={(2,1)(4,3)}

Answer 13

Sorry, we never covered inverse relations in the courses I took. But if that's true, then S^(-1) does include (6, 3).

Answer 14

well 3=6(1/2)

Answer 15

The inverse relation is not the same as the divides relation (similar, but different). Since (3, 6) is in S, by definition, (6, 3) is in S inverse.

Answer 16

okkkk i got it. Thanks You clarified matters. My book never bothered to mention that b=ka where k is an integer. Thanks for the clarification

Answer 17

No problem.