In problems 1 and 2, let A = {0, 1, 2, 3}. Draw a directed graph for each relation and determine if it is antisymmetric.

1. Let S be the set of all strings of as and bs. Defne a relation on S by s R t if and only if the length of s is less than or equal to the length of t. Is R antisymmetric? Explain why or why not.

2.R = {(0, 0),(0, 2),(1, 0),(1, 3),(2, 2),(3, 0),(3, 1)}

3.How many integers from 1 to 999 have at least one repeated digit?

4.How many bit strings have length 5, 6, 7, or 8?

5.Draw the graph G(V, E) where V = {a, b, c, d, e, f} and E = {ab, af, bc, ef, df, cd, cf}.