a. Show that ¬(p → q) and p → ¬q are logically equivalent b. Show that p –→q and ¬q → ¬p are logically equivalent. c. Show that ¬p → q and p → ¬q are logically equivalent.

Q: show that ¬( p ⊕ q)( p + q) and p.q are logically equivalent. by using logical equivalences

A: We have to prove that ¬p⊕q·p+q is logically equivalent to p·q by using logical equivalences. Note…

Q: B, Determine if the following compound propositions is a TAUTOLOGY, CONTRADICTION, or CONTINGENCY 1.…

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Q: (p V ¬r) ^ ¬((q Vr) V¬(r V p))

A: Given that proposition p is false, proposition q is true, and proposition r is false. So, ¬r is…

Q: Are the statements -(p A q) and -p Aq logically equivalent? O True False

A:

Q: e. Show that ¬(p → q) and ¬p → q are logically equivalent. f. Show that (p → q) ^ (p → r) and p → (q…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Are the following expressions logically equivalent? Could you help me create a truth table for it?…

A: Consider the given information.   Now make the true table for the given relation,

Q: 4. Show that ¬ (¬ p) and p are logically equivalent.

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Q: Show that pq and -p v q are logically equivalent.

A: To show that:p→q is logically equivalent to ¬p∨q

Q: Determine whether the following statements are logically equivalent: ~ (p → q) (~ p →~ q) V r If so,…

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Q: 2. Show that ¬(-p) and p are logically equivalent.

A: Solution:-   we know that if a statement  p is True, then its negationi.e, ¬p is false. and if pis…

Q: The contrapositive of the statement p>q is

A: If the conditional statement is  p⇒q then the contrapositive statement is  ~q⇒~p

Q: a. Show that -(p → q) and p → ¬q are logically equivalent. b. Show that p → q and ¬q → -p are…

A: This is a question of propositional logic.

Q: 3. Prove that (p A q) → ((¬p) → q) and (-p) V (¬q) are logically equivalent by using basic logical…

A: Given- (p∧q)→((¬p) ↔q)  and (¬p)∨(¬q) To prove- The above given prepositions are logically…

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

A: We need to prove the logical equivalence of: p∧q∨~p∨p∧~q≡T using logic algebra.

Q: prove that (p ↔ q) ↔ r and p ↔ (q ↔ r) are logically equivalent without using truth tables

A: (p↔q)  is a bi-conditional implication which can be written as (p→q)∧(q→p). Now combine it with…

Q: Show, by the use of the truth table/matrix, that the statement (pvq)v [(¬p)^ (¬q)] is a tautology.

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Q: Show that the following are logically equivalent 1. 2. ¬ {[(pvq)^r] v¬q} v (¬r^q) ↔ q [(p^-q) vr]…

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Q: Show that -p> (q > r) and q → (p V r) are logically equivalent.

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Q: Prove that the statements ∀x∀yP(x,y) and ∀x∀yP(y,x) are logically equivalent .

A: Given statement is ∀x∀yP(x,y)  and   ∀x∀yP(y,x)   are logically equivalent . We have to prove that…

Q: 7. Show that the following a) pV (p A q) = p b) (p A q) v (~p v (p ^ ~q)) = T are logically…

A: I have done solution step by step by mentioning all law of algebra....go through the solution

Q: 1 Show that -(pv q) and -p A-q are logically equivalent. . Show that p → q and ¬p v g are logically…

A: A statement is a sentence that can either be true or can be false but not both at the same time. But…

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: Are (p A g) and vp A ng logically equivalent?

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Q: Let P, Q and R be simple statements. Use only ONE suitable method throughout to determine precisely…

A: Tautology statement which always gives TRUTH (T) Contradiction statement which always gives FALSE…

Q: Are the following two logical equivalent  p v ~ r p ↔ r

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Q: Prove that p → q and its contrapositive logically equivalent. are

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Q: Are these statements logically equivalent? Are they satisfiable? Give your reason. ¬p → (q → r) and…

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Q: By using logical equivalences and de Morgan's rules, we can show that the statements p v q and (p…

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Q: Use a truth table to prove that (P A Q) → R and (P ^ ~R) →-Q are equivalent. logically

A: To prove: P∧Q⇒R and P∧~R⇒~Qare logically equivalent.

Q: Let P(x) denote the statement "x < 4." P(4) is A) True False

A:

Q: Indicate whether the following arguments are deductive or inductive.

A: Deductive and Inductive:-   On the off chance that the arguer accepts that the reality of the…

Q: 2. Use a truth table to justify the following logical equivalence: ~ (p → q) V r = (pV r) A (~q V r)

A: Consider ~(p→q)∨r≡(p∨r)∧(~q∨r) To use truth table to justify the logical equivalence

Q: 6. Determine whether PA ((¬P) V (¬Q))) is a tautology, contradiction, or neither.

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Q: d. (p^(p→q))→q h. A➜(~A↔(A⇒B))

A: What is Tautology: A compound statement is referred to as tautology when it is always true for every…

Q: If the proposition p → q is false then the proposition -p → ¬q must be true. O true O false

A:

Q: 2. Either show that (P → Q) → R and ~R → (P ^ ~Q) are logically equivalent or demonstrate that they…

A: We will make the truth table to examine the logical equivalence of given sentences.

Q: Is the statement ¬(¬p ^ q) ^ (p v q) logically equivalent to q?

A: Given,     ¬(¬p∧q)∧(p∨q) is logically equivalent to ____?____

Q: QUESTION 21 Determine if the following logical expression is a tautology or contradiction.…

A: Introduction: Tautology and contradiction are related with a compound logical statement. When a…

Q: 7 Show that the propositions (p Aq) and p V¬q are equivalent. logically

A: We will construct the truth table to show the logical equivalence of given two propositions.

Q: Are the statements ¬(p q) and ¬p> ¬g logically equivalent? O True O False

A: Two statements are said two be logically equivalent if their truth  table are identical.  Given…

Q: a) Show that by using Laws that if the compound statement is logically equal. [p^ (~ (~pVq))] V…

A: Given: Logical expression p∧~~p∨q∨p∧q and p. To show: p∧~~p∨q∨p∧q≡p

Q: Prove that -(p → q) + -q and T are logically equivalent by applying the laws of propositional logic.

A: Given the statement

Q: 4. Use the laws of propositional logic to prove that the following compound propositions are…

A: We will use following law  a∨~a ≡ Ta∧T≡a  a→b≡~a∨bb∧a∨c ≡(a∧b)∨(c∧b)De morgans law ~(a∧b)=~a∨~b and…

Q: Determine whether the following statements are logically equivalent: p → (q → r) (p ^ q) → r If so,…

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

Q: Use the laws of propositional logic to prove that the following compound propositions are logically…

A: 4. Given that  a) we have to show that                                    (p∨q)∧¬(¬p∧q)  and p are…

Q: Use a truth table to justify the following logical equivalence: ~ (p → q) V r = (pV r) ^ (~ q V r)

A: We have to show Left hand side is equivalent to Right Hand side using truth table.

Q: Show that ¬(p v (¬p ^ q)) and ¬p ^¬q are logically equivalent by developing a series of logical…

A: Using logical equivalences, we have to show given two expressions are equivalent.

Q: Indicate what can be deduced from the given if-then statements and fact. If A, then B, and…

A: The given statement is If A then B, and vice-versa. If B then C, and vice-versa. So, we get If B…

Q: Show that ∀ x (P(x) ∧ Q(x)) and ∀ x P(x) ∧∀ x Q(x) are logically equivalent.

A: