
I.
Test the following binary relations on the given sets S for reflexivity,
symmetry, antisymmetry, b)
S = P({a,b,c,d,e,f,g,h,i}) [ P: Power set], (A,B) belongs to R2 if and only if
A = B c) S = N [N: set of positive integers]. (x,y) belongs to R3 if and only if x^2  y^2 is even. [x^2
: stands for x squared]. ************************************************** II.
Let S = { 0,2,4,6}, and T = {1,3,5,7}. Determine whether each of the following
sets of ordered a.
{(0,2),(2,4),(4,6),(6,0)} b.
{(6,3),(2,1),(0,3),(4,5)} c.
{(2,3),(4,7),(0,1),(6,5)} ************************************************** III.
Let S = {1,2,3,4,5,6,7,8}, and let T = n. a.
How many different function can we define from S to S? b.
If n=10, how many injective functions can we define from S to T? c.
How many bijections can we define from S to S? ************************************************** IV.
You have a group of 10 men and 6 women. a)
In how many ways can you seat them in a row? b)
In how many ways can you choose a committee of 5 with at least 2 women? ************************************************** V.
A florist has roses, carnations, lilies, and snapdragons in stock. How many
different bouquets 