Discrete Mathematics Answers

Given that p and q are propositions construct the truth table of
p⟶q
p<->q

Prove that the conditional proposition p⟶q and its contrapositive ~q⟶~p

Given that p and q are propositions construct the truth table of
p -> q
p <-> q

Prove that the conditional proposition p->q and its contrapositive ~q ->~p are logically equivalent using the truth table.

Prove by mathematical induction the formula (1^3+2^3+3^3+4^3+....n^3)=(n^2(n+1)^2)/4

In how many ways can one select 7 member committee from 10 distinct persons if only three persons qualify to be chairperson?

Draw the graph represented by the adjacency matrix . (0 0 1 0 1 0 1 0 0)

Prove that for all integers n, n(n + 2)(n + 4) is divisible by 3.

Prove that for all integers a, b, c such that c =/= 0, if ac|bc then a|b.

Prove that for all integers a, b, c if a|b then ac|bc