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

Q: Show that [~q a (p → q)] →►p is tautology by constructing truth table.

A: We know that A tautology is a compound statement in Maths which always results in Truth value. and…

Q: The statement PalQv P) is tautology True False

A: Concept:

Q: Determine whether the following are tautology, contingency or contradictions. a.((~p ∧ q) ∧ (q ∧ r))…

A: The opposite of tautology is contradiction.  A contradictory statement is always false. If any truth…

Q: (g) Suppose a person claims that, "1.9% of all people in the nation always eat out Is this a…

A: Inferential statistics allows predictions based on the data where as descriptive statistics provide…

Q: (b) ¬ q V (q V p) is a tautology.

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Q: qV[~(q^r) ~q]

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Q: 5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology.

A: Question 5 is wrong, two modifications possible: Either write contradiction in place of Tautology or…

Q: Prove using truth table KB a ?

A: Here given three variables a, b and c  So using 3 variables truth table derive result

Q: suppose S(x,y) is a predicate indicating student x has taken class y. Express this in English: for…

A: Given predicate is as follows. S(x, y): Student x has taken class y. The given quantification is as…

Q: VII. Use truth table to prove that A A (B v C) = (A A B).

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Q: 13 - Which of the following is not a Tautology? I) q-> (p->q) II) (not p) -> (p->q) III) (p and q)…

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Q: Explain in this definition ”The proposition P → Q is FALSE if P is TRUE and Q is FALSE; otherwise, P…

A: A true statement/proposition is a statement that is true always whether it is written grammatically…

Q: Complete the formal proof of (~Q->~P)->((~Q->P)->Q) from no premises. The empty premise line is not…

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Q: Determine whether the given statement is a tautology, self-contradiction, or neither a tautology nor…

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Q: Show that the statement (V P(x)) V (Vx Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its…

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Q: 23. Let P, O, and R be varlab tautology. d) "(P v Q)→'P^Q

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Q: Show that [(p∨q)∧(p→r)∧(q→r)]→r is a tautology

A: To Show that [(p∨q)∧(p→r)∧(q→r)]→r is a tautology I will prove by using truth table method and rules…

Q: 3. Show that the statement p V ¬p is a tautology.

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Q: Show that [(p ∨ q) ∧ (p => r) ∧ (q => r)] => r is a tautolgy

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Q: What rule of inference has two variants where the first points out that either P and Q are both true…

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Q: write the contrapositive of: "if the earth is red, then the sky is black."

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Q: Prove this tautology using truth table: (p A r) V (r ^ q) = (p ^ q) V r

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Q: Show that the statement (Væ P(x)) V (Væ Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its…

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Q: Show that (p V q) ^(r V¬q) →(p V r) is a tautology explainig the steps taken and reason for the…

A: A tautology is a compound statement in  which always results in Truth value.

Q: The statement [- (A v B)] = [(- A) A(- B)] is a tautology O True False

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Q: 8. Show that ¬(p → q) V (-p + ¬q) is a tautology.

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Q: Show that ((p ∧ q) ∧ (p → ¬q)) ∧ (p → r) → r is a tautology using truth table

A: We have p∧q∧p→¬q∧p→r→r This will be a tautology if the value of p∧q∧p→¬q∧p→r→r is TRUE for all…

Q: Which of the following DOES NOT exhibit a tautology? (p → q) V (q → p) (p → q) ^ (q → p) С. (р ^q) —…

A: We will check this by truth tables. If value corresponding to each truth variable results in T ,…

Q: Construct the semantic tableaux for each wff to determine whether an equivalent wff exists that…

A: p∨q∧r∧~p∨~q∧~r                 ⋮p∨q∧r,~p∨~q∧~r      ⋰⋱                ⋰⋱    p   q∧r     ~p   ~q∧~r…

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

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Q: the statement Pv~(P^Q) IS tautology not tautology Skip neither tautology nor ontology

A: Tautology lagical statement

Q: Show that (p a q) → (¬ p → q) is a tautology. Show that (p → q) ^ p and (q ^ p) are logically…

A: Truth table is used to show the two statements are equivalent

Q: how to prove that contrapositive of the contrapositive is the original statement?

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Q: Q1. Decide (and justify) the following is a tautology (pA (pAr) ) → (p → q) V (pAr)

A: To check whether it is a tautology or not.

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: show that ( A u B) ˄  ( ^B u C) -> ( A v C ) is a tautology

A: Thanks for the question :)And your upvote will be really appreciable ;) For Tautology, output of…

Q: We want to find S so ((A → B) ^ A) → S is a tautology. AB(A=B) ^ A S ((A= B) ^ A) => S TT TF F T F F…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Show that [P → (QV R)] → [(P → R) V (P → Q)] is a tautology Question 5 using a truth table.

A: Given that                                  P→(Q∨R)→(P→R)∨(P→Q) we have to show by truth table that…

Q: Construct the semantic tableaux for each wff to determine whether an equivalent wff exists that…

A: According to the given information, first it is required to make the semantic tableaux for the given…

Q: 3. How to express the associativity of V as a tautology?

A: Tautology is a preposition that is always true.

Q: State, with brief reasons, whether q a [(P v q) → ] is a tautology, contradiction, or neither. a

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Q: (d) Using your ordinary language statement of (A → B) ^ A, what might you conclude? (e) What does…

A: Let us take premise A: x is a number Premise B: factors of x are 1 and x

Q: C. Define a tautology, a contradiction and a contingency.

A: We have to define Tautology, Contradiction and Contingency with examples as follows.

Q: a) Show that (a V b → c) → (a ^ b → c) is a tautology but its converse is

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Q: Is it tautology or not?

A: Given expression is ~p∧~p∨q∨q

Q: i. Determine whether (-p^(p→q)→~q)is a tautology.

A: Hello. Since your question has multiple questions, we will solve the first question for you. If you…

Q: What is the rule of inference used in the following: If I work all night on this homework, then I…

A: Rule of inference: A rule of inference are the logical forms which consists of  premises with…