For each numbered line that is not a premise in each of the formal proofs that follow state the rule of inference/replacement that justifies it. 1. (T · (UƆ V)) 2. (T ɔ (U ɔ (W·X))) 3. ((T · V) ɔ ~ (W v X)) .: (W = X) 4. ((T · U) ɔ (W ·X)) 5. (T · V) ɔ (~ W . ~ X)) 6. ((T · U) ɔ (W· X)) · ((T · V) ɔ (~ W. ~ X)) 7. (T · U v (T · V)) 8. ((W· X) V (~W v ~ X) 9. (W = X) Prompts Submitted Answers How did we arrive with line number 4? Choose a match How did we arrive with line number 5? Choose a match How did we arrive with line number 6? Choose a match

Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: We prove the given argument by using rules of inference or replacement rules.

Q: Part 2. Prove that the following are equivalent A. by Constructing a truth table 1. [p V (~ p ^q)] →…

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Q: 26. р > (qvr) qvr

A: 26.       p -> (q v r) ≡~p v (q v r) = F1       p = F2.        Resolution between F1 & F2…

Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: Note: The line 8. W·X∨~W∨~X in the proof has a mistake. It should have been 8. W·X∨~W·~X. So, we…

Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: To find- For each numbered line that is not a premise in each of the formal proofs that follow state…

Q: а. — (р @ q) + (р+q) b. (p ^ ¬q) → (p O r) → ¬p V q V ¬r с. (р — q)v(р r) —ръ(qvr) С.

A: To prove the following using equivalence law: a. ¬(p⊕q)⇔(p↔q) b. (p∧¬q)→(p⊕q)⇔¬p∨q∨¬r c.…

Q: TF r F F T If P, then Q is logically equivalent to If ~P, then ~Q. The statement ~P --> ~Q is the…

A: As per the guidelines, we can solve only 3 subparts. Please repost it with other subparts.

Q: ~M³(N-O) 1. 2. NOP 3. 0~p ✓ Conclusion /M premises prove using the rules of implication

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Q: Determine the line and the reason for the entry on line 4 given the following part of a formal proof…

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A: Simplify the logic function:

Q: 1. (¬-p → (p ^ (p ^ r)) = (¬(p ^ ¬r))

A: According to our Q n A guidelines I can solve only one question .Please upload other questions again…

Q: 1. Prove or disprove the following using either equivalence laws or truth assignments (not truth…

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Q: 12) Let X1, X2, X~N(u, 62) which the following statement true a) X-N(,82),S2~x…

A: Step 1:X1​,X2​,..,Xn​∼N(μ,δ2) independentlyThen sample meanXˉ=n∑i=1n​Xi​​We know…

Q: 4. The following are the proofing steps of an argument in formal reasoning. In proofing step 5, what…

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Q: Construct a truth table for the given starement pV~p

A: In mathematical terms, "p V ~p" means "Either 'p' is true, or its negation '~p' is true," and this…

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Q: We want to prove that (P₁ ^ P₂). P₁ → (P2) is a valid argument. Fill in the justifications at each…

A: Given:Proof of validity of the statement,…

Q: (a). Given the premises: (1) p q; (2) g(rAs); (3) -r V (Vu); (1) p^l. Conclusion: u.

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Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: We fill the given blank by using rules of inference or replacement rules.

Q: (9) 1. ~ GƆ (A v B) 2. - B 3. AƆ D 4. - G/;, D

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Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: We prove the given argument by using rules of inference or replacement rules.

Q: Determine the line and the reason for the entry on line 6 given the following part of a formal proof…

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Q: Derive the conclusion of the following argument using the method of conditional proof where…

A: Given arguments are 1. Y∨Z⊃A·B 2. B⊃Y≡D 3. Y⊃D Now,  1. Y⊃A·B∨Z⊃A·B           [Distributive property…

Q: 5. Let W(x, y) mean that student x has visited website y, where the domain for x consists of all…

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Q: Write the following arguments in vertical form and test the validity. 1. ((p → q) ^ (r → s) ^ (p V…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: T 1 T. T F T 3 T F F 4 F T F T F T D7 F F F F F 8

A: Here we have to find only the truth table for the column 4. ~q means not q i.e. if q is true then ~q…

Q: Create a proof for the following argument, using the implication rules and replacement rules. 1. (A…

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

Q: Axiom 1. A → (B → A) Axiom 2. (A → (B → C)) → ((A → B) → (A → C)) Axiom 3. (¬A → ¬B) → (B → A) Proof…

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

Q: (C v-D) ^ (B –→¬C)^ (A → D)→ (B →¬A)

A: Question: Prove the following using the IP rule C∨¬D∧B→¬C∧A→D→B→¬A

Q: PROBLEM 1. Consider [( p A (~r)) V (r^(-a))] V (~p V q), to answer the following questions: 1.…

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Q: III. From the given premise. Indicate the rules of inference used and the corresponding premises…

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Q: Consider the proposed proof of the statement Proof Statement 1. VA, B, CCU,C- (AUB) = (A - C) U…

A: INTRODUCTION Similar to basic operations on integers, set operations are a notion. Mathematical sets…

Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: The answers are written in the respective row.

Q: For each pair of statements, choose the one that is true. (a) (b) (c) (d) ○ {p} = {p, v} Ope {p, v}…

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