- #1

muso07

- 54

- 0

## Homework Statement

Let A = {a, b, c} be a set with 3 elements.

(a) How many binary relations are there on A?

(b) How many binary relations on A are reflexive?

(c) How many relations on A are symmetric?

(d) How many binary relations on A are both symmetric and reflexive?

## Homework Equations

## The Attempt at a Solution

a) There are 2^9 = 512 binary relations on A.

b) Therere are 2^(9-3)=8 relations that are reflexive.

c) Here's where I got a bit stuck, not sure if this one's right.

(i) Sets with elements of the form (x,x) 2^3 = 8

(ii) Pairs with elements of the form (x,y) (y,x) (where x /= y): (9-3)/2 = 3. Sets with these elements: 2^3 = 8.

Is that right? And how do I get the number of relations which are symmetric from that? Is it just 8x8?

d) Completely confused, I don't get any of this part.

Any help would be appreciated!