I underestimated DM, I managed to solve 7 out of 10 but these three been bugging me for days and looking online haven't helped much, can anyone help me ?
Question 1
Suppose that A is a nonempty set, and f is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs (x, y) where f (x) = f (y). Show that R is an equivalence relation on A? What are the equivalence classes of R ?
Let R be a reflexive relation on a set A. Show that Rn is reflexive for all positive integers n.
Question 2 ( This one is mostly because I've been hearing many conflicting ideas )
Which of these are posets?
- (Z, =)
- (Z, 6=)
- (Z, ≥)
- (Z, the not related to symbol )
Question 3
Let R be the relation on the set A = {1, 2, 3, 4, 5} such that (a, b)R(c, d) ⇔ a + b = c + d
- Is R an equivalence relation?
- What is the equivalence class of [(1,3)], [(2,4)], [(1,1)]?
- Find the partition of set A formed by the equivalence classes of part b.
Thanks a lot everyone. Please help me get through my exam next week. Have a nice weekend guys :)