7 DISCRETE MATH Please help me to answer this question and s

(7) DISCRETE MATH: Please help me to answer this question and show all of your work. FOLLOW MY DIRECTIONS too or I will leave negative feedback, regardless of your answer!

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(10 pts) Suppose S is a set of positive integers, and R is the following relation on S: aRb if and only if a divides b. Explain why if your answer is yes. Give a counter example if the answer is no. (a) Is R reflexive? (b) Is R symmetric? (c) Is R antisymmetric? (d) Is R transitive? (e) What is the meaning of the relation Specifically, when are two integers Rre lated? (Hint: R2-Ro R) DO NOT WRITE YOUR ANSWER ON PAPER, ITYPE IT OUT OR YOU\'LL RECEIVE NEGATIVE FEEDBACK

Solution

Suppose S is a set of positive integers,and R is the following relation on S:aRb if and only if a divides b.

a) ans:- yes, because f(a)=f(b),it follows that aRb for all set of S.

b). ans:-yes it is reflexive because suppose that aRb.since f(a)=f(b)

and f(b)=f(a) also holds and therefore bRa.

c) ans:- no ,because R is Antisymmetric precisely if for all a and b in S. if aRb and bRa, then a = b, or, equivalently, if aRb with a b, then bRa must not hold.

d)ans:- yes, suppose that aRb and bRc. Since f(a)=f(b) and f(b)=f(c),f(a)=f(c) also holds and therefore aRc.

e)

Regarding the last question, the composition of relations works as follows: if R and S are two relations over the same set, then X(SR) ,X(SR) iff there exists R such that aRb and bRa .