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)