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.