You must give us something to deal with.
Where are you haveng trouble? Show us some of your work.
Remember, we are not simply here to do your work for you.
For each of the following relations on the set of all people, determine whether it is reflexive, symmetric, antisymmetric,
and/or transitive. (Justification expected.)
a) The relation Q where (a, b)EQ if and only if a and b were born on the same day.
b) The relation R where (a, b)ER if and only if a is taller than b.
Test for reflexive: Let b = a.
Is person a born on the same day as itself? I certainly think so. Therefore, Q is reflexive.
Test for symmetric: If (a,b), then (b,a).
If person a is born on the same day as person b, is it true that person b is born on the same day as person a? This is true. Therefore, Q is symmetric.
Test for transitive: If (a,b) and (b,c), then (a,c).
If person a is born on the same day as person b, and person b is born on the same day as person c, is it true that person a is born on the same day as person c? Again, this is true. Therefore, Q is transitive.
Reflexive: is (a,a) true?b) The relation R where (a, b)ER if and only if a is taller than b.
Is person a taller than itself? Well, people have one height at any given time, so I don't think this will work. R is not reflexive.
Symmetric: if (a,b) then (b,a)
If person a is taller than person b, is person b taller than person a? Well, a is taller, then a can not also be shorter. R is not symmetric.
Transitive: if (a,b) and (b,c), then (a,c)
If person a is taller than person b, and person b is taller than person c, is person a taller than person c? Seems that the heights of a,b,c can be ranked as a>b>c, so a>c. R is transitive.