relations on sets need help asap on relations on sets

Question

this my question i dont know what to do Let A = {1, 2, 3, 4, 6} and let R be the binary relation on A defined by“x divides y”. (x divides y if and only if there exists an integer z such that xz = y). i. Write R as a set of ordered pairs.

Answer 1

Break down the components of the question. I'll start from the end.

Write R as a set of ordered pairs.

Okay, we're looking for a set of ordered pairs. An ordered pair is two values (i.e., a pair) where (1, 2) is not the same as (2, 1) — the order counts. Okay, what pairs belong in this set?

Pairs where:

x divides y if and only if there exists an integer z such that xz = y

So, in other words, "x divides y" is the same thing as saying "y can be divided evenly by x." We're used to saying it that way, but "x divides y" sure is more direct. So, 3 divides 12, 'cause "12 is divisible by 3."

Using that formal notation: "3 divides 12" specifically because I can think of a number z such that 3z = 9. What integer is that? Why, it's 4 of course!

Okay, now:

Let A = {1, 2, 3, 4, 6} and let R be the binary relation on A defined by“x divides y”

What belongs in that relation?

Answer 2

"I dont know what to do"

Just do what it says: "write R as a set of ordered pairs."

What's R? "Let R be the binary relation on A defined by 'x divides y'".

So what pairs could they mean for you to write? Clearly the (x, y) pairs comprising R.

So the answer will look like this: { (a, b), (c, d), (e, f)... }, where (a, b), (c, d) and so on are pairs of numbers, with the second one divisible by the first and both occurring in set A in that order.