let g 2 0 2 and h 4 6 8 and define a relation v from g to h as follows for every x y g h x y v m

Name: let g 2 0 2 and h 4 6 8 and define a relation v from g to h as follows for every x y g h x y v means that x y4 is an integer a is 2 v 6 21907
Uploaded: 2023-09-06T03:39:25-08:00
Duration: 4 min 31 s
Channel: Collin Parker
Description: let g 2 0 2 and h 4 6 8 and define a relation v from g to h as follows for every x y g h x y v means that x y4 is an integer a is 2 v 6 21907

Step 1: Identify the values of ( x ) and ( y ) from the relation ( V ). Here, ( x = 2 )

Let g 2 0 2 and h 4 6 8 and define a relation v from g to h...

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Transcript

00:01 For this question we are given two sets, g and h, and then we're also given a relation between them which we're calling v, and v is the set of ordered pairs in the cartesian product such that x minus y over 4 is an integer.

00:16 So there are quite a few questions to this problem.

00:20 We're going to do them slightly out of order.

00:23 So what we're going to do first is we want to find the ordered pairs that are in v.

00:30 So we're going to effectively answer part b first, and in the process that'll also give us a.

00:38 So what we're going to do, i'm going to write out the nine elements that are in the cartesian product.

00:46 So i'm going to look at all the ordered pairs that we can make.

00:56 So we should have again nine in total.

01:16 There they are.

01:26 Okay, and now we're going to do a quick check on whether or not these belong to the set v.

01:32 So again you're doing x minus y over 4, and we see if it's an integer.

01:36 So let's see, negative 2 minus 4 is negative 6, does not divide by 4.

01:42 So that one's no good.

01:45 Negative 2 minus 6 is negative 8.

01:49 That one checks out.

01:51 Negative 2 minus 8 is negative 10.

01:55 That one does not work.

01:58 All right, what else? 0 minus 4, yep.

02:02 0 minus 6, no good.

02:08 0 minus 8, that works...

Question

Let G = {−2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x, y) G ✕ H, (x, y) V means that x − y4 is an integer. (a) Is 2 V 6?

Question

Let G = {−2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x, y) G ✕ H, (x, y) V means that x − y4 is an integer. (a) Is 2 V 6?

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