QUESTION 12 Identify the law of logic used in the following simplification step: T^(p^ (qvr)) = p^ (qVr) a. Idempotent law O b. Absorption law c. Annihilation law Od. Inverse law e. Identity law QUESTION 13 Identify the law of logic used in the following simplification step: ¬ (p^q) v ¬(p^q) = ¬(p^q) a. Identity law Ob. Idempotent law c. Annihilation law Od. Absorption law e. Inverse law

Q: Q. No. 1: Prove the following using propositional logic: Prove that -[rv(q^(¬r → →p )] = ¬r^(pv¬q)…

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Q: Question 6. Use logical equivalences to show the following equivalences. Clearly indicate which law…

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Q: *Discrete Mathematics: Negation, Conjunction and Disjunction* True or False for all 1) (T ^ ~ T v ~…

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Q: 4(cos 40+ isinug) • 4 (us 110 + isin 5) leave ansuers in trigonometric form

A: r(cos θ+i sinθ)= r ei θ

Q: us the laws of propositional logic to prove

A: To Prove- Use the laws of propositional logic to prove  p ∧ q ∧ ¬r ∨ p ∧ ¬q ∧ ¬r ≡ p ∧ ¬r

Q: Let the universe of discourse be the set of all real numbers R. Use the quantifiers and logical…

A: Given: Let the universal set be ℝ(set of all real numbers.) "Every rational number is positive, and…

Q: Prove that (a ↔ a ^ b) ^ (b ↔ ¬a) = (a b) by using logical equivalences.

A: Logical equivalence is a relationship between two statements or propositions where they have the…

Q: ) True or false: The fuction -15 S-28

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Q: Consider the given statement. If Laura is not practicing soccer, then Miguel is not reading. For…

A: Given statement isIf Laura is not practicing soccer, then Miguel is not reading.Let p : Laura is not…

Q: Question 2 Use the Logical Equivalence Laws to simplify the following statement form. Be sure to…

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Q: (a) use the logical equivalences p à q ≡ ~p V  q and p ↔ q ≡ (~p V  q) ^ (~q V p) to rewrite the…

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Q: what is another  proposition that is equal to p-->(q^r^s) but only using a negation ~ symbol and ^…

A: We get the another proposition by using rules of inference

Q: 4. Verify the following identities by applying a chain of logical identities. You may use only those…

A: To Prove: the following using basic logical identities: (a) ¬(p→¬q)≡p∧q (b) p∧q∨¬p∨r≡p∧q∨r (c)…

Q: ((,ô^‚d) v (o^a)) = ((d←Ô) v (Ô←d))

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Q: i. ii. iii. Determine whether the formulae below are tautologies (A → ((¬B) V C)) → ((¬A) → B) (A →…

A: The truth table is defined as a tabular representation of the expression of all the combinations of…

Q: Simplify (-mvs)^-(mas) to ¬m 1. Select a law from the right to apply (-mvs)^-(mas)

A: We have ¬m∨s∧¬m∧s                       (1) By De Morgan's law ¬(a∧b)=(¬a∨¬b), we can write…

Q: Consider the argument: Premise 1: p→q Premise 2: ~r Premise 3: qvr Conclusion: r Write the above…

A: If we are given with certain premises and a conclusion, it states that the meet of all the premises…