IILM University, Greater Noida Unit-I Worksheet PDF

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 𝐵 = { 2, 4, 5, 6} (i). (∃ 𝑦 ∈ 𝐵)(𝑦 + 4 = 10 ) (ii). (∃ 𝑥, 𝑥 ∈ 𝐵)(𝑥 + 2 = 15) 5. Let R(Y) denotes the statement “the word Y contains the letter ‘o’ ”. What are the truth values of P(Lemmon), P(Orange), P(Apple)?. 6. Let 𝑃(𝑋, 𝑌) be a statement 𝑋 + 𝑌 + 𝑋𝑌 − 1. Find the value 𝑃(1, 2) and 𝑃(6, −5). 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) 𝐵 ∨ (𝐴 ∧ ¬𝐵) ∨ (¬𝐴 ∧ ¬𝐵). (ii) (𝐴 → 𝐵) ∧ (𝐵 → 𝐶)} → (𝐴 → 𝐵). (iii). (𝑄 𝑉 𝑃)⋀ (𝑄 𝑉 𝑅) ∧ (¬ (𝑃𝑉 𝑅) 𝑉 ¬𝑄)). (iv). (𝑃 → (𝑄 → 𝑅)) → ((𝑃 → 𝑄) → (𝑃 → 𝑅)) 3. Check the below compound propositions are equivalent or not. (i). ( 𝑃 → 𝑄) and (¬ 𝑃 𝑉 𝑄 ). (iii). 𝑃 ∧ ¬(𝑄 ∨ 𝑃) and (𝑃 ∧ ¬𝑄) ∨ 𝑅). (iv). 𝑃 ∨ ¬(𝑄 ∧ 𝑅) and (𝑃 ∨ ¬𝑄) ∨ ¬𝑅). 4. Write the rules of theory of inference. And solve Given the premises “ A student of this class has not read the Discrete mathematics text book” and “Everyone in this class passed the first unit test” show that “someone who passed the first unit test has not read the discrete mathematics book”. 5. (a). Find whether the following argument is valid or not “ No Engineering student is bad in studies “ “Anil is not bad in studies” Therefore “ Anil is an engineering student”. (b). Prove that the following argument is valid: “all Linos are carnivorous. “some animals are Linos.” 1