For each relation in Question 1-Quesiton 4 specify all the properties:

reflexive, antisymmetric, symmetric, transitive they have.

Question 1: Let A = { set of all people }, relation R: A x A where

R = { (a,b) | a is at least as tall as b }

Question 2: Set S = { 0,1,2,3 } , relation R: S x S is defined as:

    (m,n) epsilon R if m + n = 4;

Question 3: Z is the set of integers. Relation R: Z x Z is defined as:

    x,y epsilon Z; (x,y) epsilon R, x is a multiple of y;

Question 4: Z+ is the set of positive integers, relation R: Z+ x Z+,

a,b,c,d epsilon Z+; (a,b),(c,d) epsilon R  if an only if

    a + d = b + c.

Question 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.

These problems are complex and I don't know how to do it.