So some equations are easy to understand and figure out. But, my lack of understanding of the basic info makes a lot of questions very hard:
for reflexive its pretty easy all i have to do is change y to x and see if both sides are equal. however, for example for X is the set of prime numbers greater than 2 and xRy (x+y)/2 is prime so i need to prove reflexive but x+y need to be odd+even so that its divisible of 2 is prime so taking x as odd proves it right but taking x as even gets us even makes me confused.
for transitive all i have to do is prove there is a relation between x and c through y and c and x and y but a lot of answers say 1R0 0R1 implies 1R1 isn't transitive and i do not get it when to use this way for example Let X be a nonempty set of positive natural numbers and let R be the binary relation defined by xRy ∃n ∈ ℕ* y=x^n 1. prove that R is an order relation
so i should do z=x^n^n thus proving it transitive or should i say z=x^n proving it not transitive.
for symmetric and anti symmetric its i should switch them x and y with each other and if they were the same in all cases then its symmetric. if there was one case then that means its anti symmetric like x=y is the only way we will get the same answer.
so basically, unless i memorized the way of solving of each type of question ill get lost in what to do and how to prove it. hope someone can clear up my misunderstanding about this topic.