Question 3. Show that [p ^ (p^q)] V (p→q) is a tautology using logical equivalences. for a list of applicable laws and definitions.) Make sure to clearly state which definitions/laws you have used in each step of your work

Q: It says "Then there must exists some Aj which covers 0". Why 0? I don't understand. Please explain

A: You can take any point x in [0,1].  There exist a Aj which covers x.

Q: 26) Let "" denote the truth-functional connective "exclusive OR." and let "A,1 "v, " and -" denote,…

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Q: Step 1 of 1 A An equivalence relation R on a set S is one that satisfies these three properties for…

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Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

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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

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Q: Prove that the following statement is a tautology (~q^(p⇒q)) ⇒~p

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Q: a Prove that the interval [-1, 2] is a closed set in R. Explain each step in your argument.

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Q: Question 2 Use the Logical Equivalence Laws to simplify the following statement form. Be sure to…

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Q: Determine in set notation where Continuas nuuas S! x^~X + E =X)

A: Given , f(x) = 3 + x2 - √x We have to determine where the function is continuous

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…

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Q: defined are the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

A: A relation R on a set X is a subset of X×X. That is R⊆X×X. (b). Let ≡6 and ≡10 are two subset on the…

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Q: Prove the given expression is a tautology by developing a series of logical equivalence to…

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Q: Let F(x, y) be the statement x can fool y, where the domain consists of all people in the world. Use…

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Q: Jsing equivalence laws, show that p(p → q) = ¬(p^q).

A: Introduction: A truth table demonstrates how the truth or falsity of a compound statement is…

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A: Case (i) : Let . If x is positive real numbers , then multiplying it by itself than it will be…

Q: -(pV ~q) V (~ p^ ~ q) =~ p 2.

A: We will prove this using the logical equivalence laws given in the question.