IILM University, Greater Noida Unit-I Worksheet PDF
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This is a worksheet with short and long answer questions on logical concepts including propositions, quantifiers, predicates, and inference rules. It's suitable for undergraduate-level study.
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IILM University, Greater Noida Unit-I Short Answer Questions 1. Define the following (i).Simple proposition, (ii) compound proposition (iii) logical connections such as conjunction and disjunction, conditional, bi-conditional ,converse, inverse, c...
IILM University, Greater Noida Unit-I Short Answer Questions 1. Define the following (i).Simple proposition, (ii) compound proposition (iii) logical connections such as conjunction and disjunction, conditional, bi-conditional ,converse, inverse, contrapositive, negation and equivalent. 2. Define Tautologies,and contradiction. 3. Explain Quantifiers and types of Quantifiers with example. 4. Write the truth value of the below statements for the set π΅ = { 2, 4, 5, 6} (i). (β π¦ β π΅)(π¦ + 4 = 10 ) (ii). (β π₯, π₯ β π΅)(π₯ + 2 = 15) 5. Let R(Y) denotes the statement βthe word Y contains the letter βoβ β. What are the truth values of P(Lemmon), P(Orange), P(Apple)?. 6. Let π(π, π) be a statement π + π + ππ β 1. Find the value π(1, 2) and π(6, β5). 7. Expalin Predicates. Write the rule of Modus tollens of predicates and write the rule of Modus Pones of predicates. Long Answer Questions 1. Show that the following propositions are tautology or contradiction 2. (i) π΅ β¨ (π΄ β§ Β¬π΅) β¨ (Β¬π΄ β§ Β¬π΅). (ii) (π΄ β π΅) β§ (π΅ β πΆ)} β (π΄ β π΅). (iii). (π π π)β (π π π ) β§ (Β¬ (ππ π ) π Β¬π)). (iv). (π β (π β π )) β ((π β π) β (π β π )) 3. Check the below compound propositions are equivalent or not. (i). ( π β π) and (Β¬ π π π ). (iii). π β§ Β¬(π β¨ π) and (π β§ Β¬π) β¨ π ). (iv). π β¨ Β¬(π β§ π ) and (π β¨ Β¬π) β¨ Β¬π ). 4. Write the rules of theory of inference. And solve Given the premises β A student of this class has not read the Discrete mathematics text bookβ and βEveryone in this class passed the first unit testβ show that βsomeone who passed the first unit test has not read the discrete mathematics bookβ. 5. (a). Find whether the following argument is valid or not β No Engineering student is bad in studies β βAnil is not bad in studiesβ Therefore β Anil is an engineering studentβ. (b). Prove that the following argument is valid: βall Linos are carnivorous. βsome animals are Linos.β 1
