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VXL TUTORIAL : COMPUTER CLASSES BY VINOD KHARE PH: 9336061496, Assignment Sheet -1, Proposition Logic, Question 1:, If (~P ⇒ Q) then write its :, (i) Inverse, (ii) Converse, Question 2:, The statements are given as:, If p : Jitendra Kumar is a computer teacher., q : Rahul is a student., Write these statements in symbolic form:, (a) Jitendra Kumar is a computer teacher and Rahul is a student., (b) Jitendra Kumar is a computer teacher and Rahul is not a student., (c) Jitendra Kumar is not a computer teacher and Rahul is a student., (d) Neither Jitendra Kumar is a computer teacher nor Rahul is a student., (e) Either Jitendra Kumar is a computer teacher or Rahul is a student., Question 3:, Show that X v ~ (Y ^ X) is a tautology., Question 4:, State whether the following expression is a Tautology, Contradiction or the, Contingency with help of the truth table., (X→Z) v ~[(X→Y) ^ (Y→Z)], Question 5:, The statements are given as:, If p : Today is a holiday., q : I will go to attend a birthday party., Express each of the following statement in words:, (a) p v ~ q

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VXL TUTORIAL : COMPUTER CLASSES BY VINOD KHARE PH: 9336061496, (b) ~q, (c) (~p) ^ q, (d) ~(p v q), (e) ~((~p) ^ q), (f) (~p) . ~q, Question 6:, Consider the statements:, If p : You work hard., q : You will succeed in your life., Translate each of following symbolic expressions in meaningful sentences:, (a) p ⇒ q, (b) q ⇒ p, (c) (~p) ⇒ (~q), (d) (~q) ⇒ (~p), Question 7:, Construct the truth tables for the following:, (a) (p ⇒ q) ^ (q ⇒ p), (b) q ⇒ [(~p) v q], Question 8:, Verify the following proposition with help of the truth table:, P v (~P ^ Q) = P v Q, Question 9:, Write converse, inverse and contrapositive of each statement:, (a) If it rains, then you will not play., (b) If you work hard, then you will pass., (c) If I run fast, then I will win the race., Question 10:

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VXL TUTORIAL : COMPUTER CLASSES BY VINOD KHARE PH: 9336061496, Show that the given statements are tautologies:, (a) [(p ⇒ q) ^ (q ⇒ r)] ⇒ (p ⇒ r), b) [(p ⇒ q) ^ p] ⇒ q