1. Prepare the
truth table of the following statement patterns.
i. (p∧q)→~p.
ii. (p→q)↔(~p∨q)
iii. (~p∨q)∧(~p∧~q)
iv. (p↔r)∧(q↔p)
v. (p∨~q)→(r∧p).
2. Examine,
whether each of the following statement patterns is a tautology, or a
contradiction or a contingency.
(p∧q)∨(~p∨~q)
(p∧~q)↔(p→q)
(p∨q)∧~(p∧q)
(p∧q)∨(p∧r)
3. Prove that each of the following statement patterns is a tautology.
(i) (~p∨q)∨(q→p)
(ii) (q→p)∨(p→q)
(iii) (q→r)∨(r→p)
4. Prove that each of the following statement patterns is a contradiction.
(i) (p∧~q)∧(p→q)
(ii) (p∧q)∧(p→~q)
(iii) (~p∧~q)∧(q∧r)
5. Show that each of the following statement patterns is a contingency.
(~p→q)↔(p→q)
(~p∨q)→[p∧(q∨~q) ]
(~p→q)∧(p∧r)
6. Using truth table verify.
~(p→q)≡p∧~(~q)≡p∧q
~(~p→~q)≡~p∧q
p∧(~q∨r)≡~[p→(q∧~r)]
7. Prove that the following pairs of statement patterns are equivalent.
p→(q→p)and ~p→(p→q)
(p∨q)→r and (p→r)∧(q→r)
(p∨q)→r and (p→r)∧(q→r)