Show that: x x C not= A x x C).

Let R be a binary relation defined as

R E R^2 a 3}.

Determine whether R is reflexive, symmetric, or anti-symmetric.

If in a group a^5 aba^-1 for b EG, find order(b).

Prove that the product of disjoint cycles is commutative.

Every field is an integral domain, prove it.

If R is a ring such that V a E R,then prove that

a a 0 V a E R

a b a

Construct the truth table for

1 R).

Prove that the pentagonal lattice is not modular.

Show that V 1 l Q P is a logical implication.

Write the conjunctive normal form of the function f

Convert the DNF
xyz xy'z into CNF.

Simplify the Boolean function:

13, 15).

Show that Kn a Hamiltonian circuit whenever

Show that a simple graph G is a tree, iff there is one path between every pair of vertices.