Question

Discrete Mathematics. Let A = {2,4,6,8,10}, and define a relation R on A as ∀x,y ∈...

Discrete Mathematics.

Let A = {2,4,6,8,10}, and define a relation R on A as ∀x,y ∈ A,xRy ↔ 4|(x−y).

(a) Show R is an equivalence relation.
(b) Give R explicitly in terms of its elements.
(c) Draw the directed graph of R.
(d) List all the distinct equivalence classes of R.

1 0
Add a comment Improve this question Transcribed image text
Answer #1

Solution Let A = {2,4,6,8,10} to, y EA x Ry~4 | (x-y) R is reflexive Х consider belongs to R, 4167-7)=0 x 12 x SO Symmetric a© 4 4 6 8 8 10 10 ANI the distinct equivalence Classes of R is R = {(2,6), (2,10), (4,8),16,10), 110,4)} give like Pleose if

Add a comment
Answer #2

solution: Page 1 * Given a) Reflexive porpesty: Consider x belongs to R, =o, which is an integer, so then h/(x-x) XRx. symmetPage-2 b) As per equation, the elements need to be divided by hi So R={(2,6), (2,6), (418), (6,2), (6, 1), (8,4), (10,2), (10c)2 2 4 6 6 8 8 10 10

d ) 2) Distinct equivalence classes of R, So R = {(2,6), (2, 6), (4,8), (6,10), (10,4)} Х Please give me Positive like.

Add a comment
Know the answer?
Add Answer to:
Discrete Mathematics. Let A = {2,4,6,8,10}, and define a relation R on A as ∀x,y ∈...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT