Show that `~(p ltimplies q) -= p ltimplies ~q`

Show that (i) ~(p wedge q) -= ~p vee ~q (ii) ~(p to q) -= p wedge~q .

Show that -(p leftrightarrow q) -= p leftrightarrow -q .

Each of the statement p implies~q,~rimplies q and p is true. Then

Show that ~(p harr q) -= ( p ^^ ~q) vv(~p ^^q) .

Prove that ~(~pto ~q) -=~p ^^q

Show that (p ^^ not q) vv ( not p vv q) is a tautology.

Show that (pvvq) to r -= (p to r) ^^ (q to r)

Prove that ~((~p)^^q) -=pvv(~q) .

Let p: Jupiter is a planet and q: India is an island be any two simple statements. Give verbal sentence describing each of the following statements: (i) ~p (ii) p wedge ~ q (iii) ~p vee q (iv) p to ~q (v) p ltimplies q

Show that ( p ^^ q) to (p vv q) is a tautology.