- #1
muso07
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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!