Show each of the following is valid using Rules of Inference and Laws of Equivalence: r v ~p -p = s

Q: What is the equivalence of ( ¬ (( P → Q) ∧( Q → P))) ↔ ( Q → P)?

A: the equivalence of ( ¬ (( P → Q) ∧( Q → P))) ↔ ( Q → P) is to be computed below .

Q: Prove the following using equivalence laws: (a) (¬A∨A∨¬B) ∧ (¬(A∧B) ∨¬A) ∨C≡ (A∧B) →C   (b) ¬(B→C)…

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Q: prove the following logical equivalence: p Vq = ~p→q

A: Question: Prove the logical equivalence p∨q≡~p→q

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: Suppose that the follow set relations are true: M C F RC F R+ M Rn M # Ø е€ (R- M) Is it true that e…

A: 1. For the given conditions M⊂F, R⊂F, R≠M, R∩M≠∅, e∈(R-M). Here e∈(R-M) ⇒e∈R ∩M'⇒e∈R and e∈M'⇒e∈F…

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

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Q: Let A,B,C,D be set. Prove that (A x B) \ (C x D) = [(A\C) x B] or [A x (B\D)] Kindly Indicate the…

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Q: The following is a logic question, show that: (A → C) ∧ (B → C) ≡ (A ∨ B) → C Clearly indicate…

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Q: Show that (r ∨ ¬s) ∧ (r ∨ s) ≣ s using logical equivalence laws

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Q: Validate the following argument form using inference laws. pVr -qVs pAq -(r-s)

A: F1 : ~p V r F2 : ~q V s F3 : p ∧ q      : p [F3a]   &   q [F3b] Goal, G : ~(r -> ~s)…

Q: When we use absorption law to p V (p Λ ¬q) which of the following is the logical equivalence…

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Q: Which of the following statements must be true? Select all that apply?

A: Given, A triangle IJK with altitude JL   IJ = JK   JL ⊥ KI  and  JL bisects IK  perpendicularly IL =…

Q: Prove the following using natural deduction. (b) -А — (А > В)

A: We prove this by using rules of inference.

Q: P) P pV q + q V p (p^q) ^r + p ^ (q^r)

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Q: Let R={y,p}, S={z,p,u}, and T={r,y,p,u,z}, For each of the following questions, enter T if the…

A: Given that R={y,p} ,S={z,p,u} ,and T={r,y,p,u,z}1) R has the element y, but S does not have y in it.…

Q: Prove the following statements (Premises) using the natural deduction laws: Premises Conclusion D>…

A: Given to prove:  D→A∧BB→L∧M              D     M Proof: I. If D, then A∧B that is both A and B. II.…

Q: 2. Prove the following using natural deduction. (f) Given A B, show ¬A ¬B (g) Given A- C and B D,…

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Q: Determine whether statements P, 4, and 7 each need to be true or false to make the statement below…

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Q: Q >S, F R -SVR, QvR

A: We have to prove that by using rules of inferences that Given argument is Valid.

Q: Determine if the following formula is a tautology, contradiction, or neither. (p∧q)⊕(¬p∨¬q)

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Q: Is the following argument valid? Provide a proof for your answer. p =⇒ (q ∧ r)  ∼q − − − − − − − − −…

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Q: P→-Q,QVS, T→S EPVT→S

A: We prove by applying the rules of inference whether this argument is Valid or not.

Q: The transitive property of equality states that if AB = BA, then BA = AB. %3D %3D O True O False

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Q: Identify the axiom or postulate that applies to the following statement.     If m = n, then m – z =…

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Q: prove the logical equivalence: a) [p^(p>q]]>q is tautology

A: We use truth table here

Q: Use the rules of inference to show that if the following premises are given • Vr(P(x) ^ R(x)) •…

A: GivenP(x)→(Q(x)∧S(x))P(a)→(Q(a)∧S(a)) for any  a  in the domain  ...Universal  on…

Q: Consider the following proof of that IS supposed to prove the tautology: (A v B → C^ D) → (B → D)…

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Q: (p^ (~(~pV q))) v (pAq) = p.

A: Introduction :-  Given :-  We have to show logical equivalence of two statement patterns.

Q: Determine whether the following statements are logically equivalent. Provide a justification for the…

A: We have to show whether ~p∨~p∧q   and  ~p∧~q are equivalent or not.

Q: Show that the following statement is a tautology using the proof method. You will need to use one or…

A: We have to show that the following statement is tautology using the proof method.

Q: Which of the following statements are tautologies? Mark all correct answers Select one or more: O (p…

A: handwriting solution

Q: Use rules of inference to show that if ∀x(Y(x) → (Q(x) ∧ S(x))) and ∀x(Y(x) ∧ R(x)) are true, then…

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Q: prove that each wff is a valid argument. (∃x)(∃y)P(x, y) →  (∃y)(∃x)P(x, y)

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Q: 1. Show that the following pairs are logically equivalent: a. P^ (Q V R); (P^ Q)V (P ^ R) b. P v (Q…

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

Q: P V Q =>R, A =>-R, A VD EP >D

A: let  P1:P∨Q⇒RP2: A⇒-RP3: A∨D |-P⇒D Using P1:P∨Q⇒R P∨Q⇒R=¬P∨Q∨R               =¬P∧Q∨R…

Q: Provide the steps and reasons to establish the following logical equivalence: [(-p v ¬4)→…

A: To establish the logical equivalences of the following: A. ¬p∨¬q→p∧q∧r⇔p∧q B. p∧¬q→r∧r∨¬q∨r∧s∨r∧¬s⇔p

Q: 3. Use our known logical equivalence rules to show the following equivalence: - (p ^ (qV ~ p)) = ~…

A: Boolean algebra is a branch of mathematics that is concerned with binary variables and operations on…

Q: Show the logical equivalence of the following 7. (p v q) V r = p V (q V r) 8. (p A q) ^ r = p ^ (q ^…

A: Since you have posted multiple questions and need answers for multiple questions but we can answer…

Q: Question 8. A Compound proposition that is neither a tautology nor a contradiction is called.. . A.…

A: Definition of Contingency: A compound proposition that is always true for all possible truth values…

Q: prove these deductions (a) x∩y=∅, (z⊂x), ∴(z∩y)=∅ (b) p⊂q, ∴(r∖q) = (r∖p)∖q

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Q: Use the 18 rules of inference to derive the conclusions of the following symbolized arguments. A.…

A: Answer for sub question 1: Since, S∧K→R, by conditional disjunction it follows that ¬S∧K∨R holds…

Q: 6. Use the rules of inference from the formula sheet to show the follow argument is valid: \x Q(x)…

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Q: Determine whether each of the following statements can prove that a || b .Use the dropdown menu to…

A: a)m∠2≅m∠7 This can not prove that a||b.

Q: C. Provide the steps and reasons to establish the following logical equivalence: 1) [-pv¬g)→(p…

A: As per our guidelines we are supposed to answer only 1st question. Kindly repost other parts in the…

Q: Which of the following proofs makes use of arrows in the proof? O Indirect proof O Flow proof O…

A: topic - different types of proofs A flow proof use diagram to show each statement leading to the…

Q: 3. Use our known logical equivalence rules to show the following equivalence: ~ (p^ (qV ~ p)) = ~ pV…

A: For any two statements p and q, to prove ¬p∧q∨¬p≡¬p∨¬q L.H.S ¬p∧q∨¬p≡¬p∧q∨p∧¬p…

Q: If R is reflexive, then R is reflexive. O True O False

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Q: Match the logical equivalence on the left with its name on the right. Instructions PAT = p pv T=T…

A: Explanation of the answer is as follows