Problem:

Question:- For each relation specify all the properties: reflexive, symmetric, antisymmetric, transitive they have.

Part 1- Let A = { set of all people }, relation R: A x A where R = { (a,b) | a is at least as tall as b }

Part 2- Set S = { 0,1,2,3 } , relation R: S x S is defined as: (m,n) E R if m + n = 4;

Part 3- Z is the set of integers. Relation R: Z x Z is defined as: x,y E Z; (x,y) E R, x is a multiple of y;

Part 4- Z+ is the set of positive integers, relation R: Z+x Z+, a,b,c,d E Z+; (a,b),(c,d) E R if an only if a + d = b + c.

Part 5- R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S = {(2,1},(3,1),(3,2),(4,2)}. Find S o R, R o S, R-1, S-1,where o means composition.

Please show all the calculations step by step.