# Thread: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b

1. ## Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b

Q: Let S = {1,2,5,6 }
Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)

2. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Since multiplying any integer by an even integer results in an even integer, you just need to make sure that if (x,y) is in R, then at least one of x or y is even. For example, it would be okay to have (2,5) in R, but it wouldn't be okay to have (1,5) in R. There are lots of choices for R here. For example, we could let R={(1,2),(2,1),(2,2),(2,5)}.

3. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Please solve my question in proper method.

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4. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Originally Posted by sMilips
Please solve my question in proper method.
Surely you are in no position to make a demand? So who is to say what is proper?

$\mathcal{R}=[\mathit{S}\times\{2,6\}]\cup[\mathit{S}\times\{2,6\}]^{-1}$

5. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Originally Posted by Plato
Surely you are in no position to make a demand? So who is to say what is proper?

$\mathcal{R}=[\mathit{S}\times\{2,6\}]\cup[\mathit{S}\times\{2,6\}]^{-1}$
I mean solve in suitable method.

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6. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Originally Posted by sMilips
I mean solve in suitable method.
You asked for our help, did you not?
Then you demand a different more "standard" answer. I asked who you were to do that.
Then I gave you the complete answer that accounted for the 'iff' part of your question.
But you seem to not understand even that correct answer.

7. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Originally Posted by DrSteve
Since multiplying any integer by an even integer results in an even integer, you just need to make sure that if (x,y) is in R, then at least one of x or y is even. For example, it would be okay to have (2,5) in R, but it wouldn't be okay to have (1,5) in R. There are lots of choices for R here. For example, we could let R={(1,2),(2,1),(2,2),(2,5)}.
But 2x5=10 and 2x2=4.. 5 and 4 are not members of given set.

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8. ## Re: Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as

Originally Posted by sMilips
But 2x5=10 and 2x2=4.. 5 and 4 are not members of given set.
That has nothing to do with the posted question.
Originally Posted by sMilips
Q: Let S = {1,2,5,6 }
Define a relation R on S of at least four order pairs, as $(a,b) \in R \iff a\cdot b\text{ is even}$ (i.e. a multiply by b is even)
.
BUT the if an only if requires that the entire relation be listed.