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: Show that the following are logically equivalent using logic algebra a) pv (p^q) = p b) (p^q) v (~pv…

A: To Show- Show that the following are logically equivalent using logic algebra. p ∨ p ∧ q ≡ p p ∧ q…

Q: proofl Ant>pl An

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Q: Use a sequence of logical equivalences to show that (p → q) ^ (p → r) and p → (q ^ r) logically…

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Q: Use the laws of logic to simplify ¬[q→¬(p^q)].

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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: 1. (a) Give the definitions of Boolean connectives ¬, A, V,→, + as truth functions F, FA, Fy, F=,F»…

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Q: (¬AUB→(CND))(¬AUB→(CND)) ¬AUB→CND¬AUB→CND (¬AUB)→(CND)(¬AUB)→(CND) ¬AU(B→C)ND they saying the same…

A: We have to show the following expressions are equivalent or not 1. (¬A∪B→(C∩D))2. ¬A∪B→C∩D3.…

Q: Statement 1 - If you study hard, you get good marks Statement 2:- If you get good marks, you get…

A: Introduction: A compound assertion that is true for each value of the component statements is…

Q: 1. (a) Give the definitions of Boolean connectives , A, as truth functions F, FA, Fv, F→, F» of…

A: 1 (a) Modern texts on logic typically take as primitive some subset of the connectives: conjunction…

Q: 3. Is the Boolean expression (~ p^q)^~r the negation of p V (q ⇒r)? Explain.

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Q: i) ii) ¬(P V Q) ^ ¬(РЛQ) ¬(P^ Q ^R) V (P^ ¬Q ^R) V (Р^ ¬Q^ ¬R)

A: Given: Let us consider the given Boolean expressions, i) ~P∨Q∧~P∧Q ii) ~P∧Q∧R∨P∧~Q∧R∨P∧~Q∧~R

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: I need help in simplifying this using the Logical Equivalence Rules (De Morgan's Laws etc.) [(~p ^…

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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: 1. (a) Give the definitions of Boolean connectives , A, V,=, + as truth functions F-, FA, Fv, F=, F…

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

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Q: Question 3 This ~(a → b) = a ^ ~b is a logical equivalence. True False

A: We need to see if ~a→b≡a∧~b is logically equivalent. To see if they are logically equivalent we need…

Q: 19) Define an appropriate language and formalize "There is a student who is loved by every other…

A: Given Statement "There is a student who is loved by every other student" Third FOL formula is…

Q: Show that (p →q) and p ^-q are logically equivalent.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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: EIf a,,a,,a,.--,a, be an A P of non - zero terms, prove that ------ 1 1 +. 1 n-1 %3D a,a, a,a, a,a,

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Q: Write the truth-functional form (TFF) for each sentence. Use P, Q, R, etc. as replacement letters.…

A: Since you have posted a multi sub part question according to guidelines I will solve first three…

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: II. Prove/Disprove: 1. (¬A → → ¬B) + (¬C A A) = ¬ (A V –¬B) + (В — С)

A: We will check whether the given statement is equivalent or not.

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: Is (A⇒ (BAC)) ((A^¬C) V (A^¬B)) a tautology, a contradiction, or a contingency? O contradiction O…

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Q: Question 2 Is (p → q) why not? (-q → -p) a tautology? Why or

A: Note:- As per our guidelines, we can answer the First part and its sub parts only if any particular…

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: i) ii) (P V Q) ^ -(P AQ) (P Λ Ο ^ R) V (P ^ →Q ^ R) V (Ρ ^ ¬Q ^ ¬R)

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Q: (p ^ ¬p) v (q ^ ¬q) v (r ^ ¬r) is O Tautology O Contradiction O Contingency O None of the choices

A: Given preposition (p∧¬p)∨(q∧¬q)∨(r∧¬r) We know If the proposition is true in every row of the truth…

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: Show that the A is logically equivalent to B using logic equivalence laws. A.) (p+q) B) (qr) Vv(prq)…

A: The bidirectional implication is defined as p↔q ≈p→q∧q→p And unidirectional is defined as p→q≈(~p∨q)…

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…