Prove that the relation of similarity in the set of all triangles in a plane is an equivalence relation.

Prove that n where B and C be any sets.

If G is a group such that for three consecutive integers n for all a,b € show that G is abelian.

Prove that the intersection of any two subgroups of a group G is again a subgroup of G.

Show that it is not necessary that union of two sublattices is again a sublattice.

Express the following function in disjunctive normal form

z

Prove that P Q Q).

Show that Q V Q is a tautology.

Use induction to prove that any integer n 2 is either a prime or a product of primes.

Prove that two graphs are isomorphic, iff their complements are isomorphic.

Find the chromatic polynomial of K4,complete graph of 4 vertices.

Give the set of those real numbers x for which the truth value of p q is true, where x ­2 and q x 3 7

Define path, walk, connected graph, tree and give examples.

Prove that the pentagonal lattice is not modular.