In the following relation {(a, a),(a, b),(b, a),(b, b),(b, d),(c, c),(d, b),(d, d)} A = {a, b, c, d}, which of the following is not true?

• this relation is not reflexive, since (a, a),(b, b),(c, c),(d, d) R.
• this relation is not transitive, since (a, b) and (b, d) are in R but (a, d) / R.
• None of these
• this relation is symmetric since the reverse of every non-reflexive element is present.

A number of edges incident with the vertex V is called?

• 1 point
• Degree of a Graph
• None of the above
• Degree of a Vertex
• Handshaking Lemma

Given the relation S = {(1, 1),(1, 3),(2, 1),(2, 2),(2, 3),(3, 3),(4, 4)} on the set A = {1, 2, 3, 4}: Which of the following is not true?

• S is antisymmetric.
• S is transitive
• S is not symmetric
• S is irreflexive

For which of the following does there exist a graph G = (V, E, ) satisfying the specified conditions?

• A graph with 9 vertices, 9 edges, and no cycles.
• A graph with 5 components 12 vertices and 7 edges.
• A graph with 5 components 30 vertices and 24 edges.
• A tree with 9 vertices and the sum of the degrees of all the vertices is 18.
• A connected graph with 12 edges 5 vertices and fewer than 8 cycles.

A small deck of five cards are numbered 1 to 5. First one card and then a second card are selected at random, with replacement. What is the probability that the sum of the values on the cards is a prime number?

• 11/25
• 13/25
• 10/25
• 12/25
• 14/25