### LOGIC EX. NO. 1.6

1. Prepare the truth table of the following statement patterns. [VIDEO PART ONE] [VIDEO PART TWO] [VIDEO PART THREE]

i. (pq)→~p.

ii. (p→q)↔(~pq)

iii. (~pq)(~p~q)

iv. (p↔r)(q↔p)

v. (p~q)→(rp).

2. Examine, whether each of the following statement patterns is a tautology, or a contradiction or a contingency. [VIDEO PART ONE] [VIDEO PART TWO]

(pq)(~p~q)

(p~q)↔(p→q)

(pq)~(pq)

(pq)(pr)

3. Prove that each of the following statement patterns is  a tautology. [video part one] [video part two]

(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. [video]

(i) (p~q)(p→q)
(ii) (pq)(p→~q)
(iii) (~p~q)(qr)

5. Show that each of the following statement patterns is a contingency. [Video part one] [Video part two]

(~p→q)↔(p→q)
(~pq)→[p(q~q) ]
(~p→q)(pr)

6. Using truth table verify.  [video part one] [video part two]

~(p→q)≡p~(~q)≡pq
~(~p→~q)≡~pq
p(~qr)≡~[p→(q~r)]

7. Prove that the following pairs of statement patterns are equivalent. [video]
p→(q→p)and ~p→(p→q)
(p∨q)→r and (p→r)∧(q→r)
(p∨q)→r and (p→r)∧(q→r)