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

Q: Direction

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Q: Prove that neQ

A: Given ddxxn=nxn-1

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Q: Show that (p  →  q)^(p  →  r) and p  →  (q ∨r) are logically equivalent.

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Q: i) Determine the domain of ) (x). In 1-2 sentences axnlnin

A: Solution is attached below.

Q: does not exist

A: Given that:  The limit   lim(x,y)→(0, 0 ) x2 + yx2 + y2   .

Q: of the propositional equivalences. Don't use a truth ta

A: Introduction: The following equivalence laws, we will use in this problem. The implication law…

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…

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A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

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Q: 22. Show that (p ^ q) → (p V q) is a tautology 23. Show that ¬(p V (¬p ^ q)) and ¬p ^ ¬q are…

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Q: A postulate is a statement or concept that is generally accepted among mathematicians but is not…

A: Given query is to find the statement is true or false .

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A: Find the smallest equivalence relation such that { (a,b), (a,c), (a,d), (d,e) } is a subset of…

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

Q: Prove the following argument is invalid by finding a quantificational model in which all the…

A: The given premises and conclusion are as follows. Premise 1: ∀xSx∧Px→Rx Premise 2: ∀xTx→¬Rx∧¬Px…

Q: Prove that (Pv Q) (Q v (P (Q R))) is tautology without using truth table (use logic rules only) 14

A: Given:

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A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

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: 5) Verify the logical equivalence (p ^q^ ¬r) V (¬p ^ q ^ ¬r) = q ^ ¬r by using known logical…

A: ACCORDING TO BARTLEBY GUIDELINES, SOLUTION OF ONLY FIRST QUESTION WILL BE PROVIDED.

Q: Discuss the logical basis for a direct proof and an indirect proof by citing specific logical…

A: To Discuss: The logical basis for a direct proof and an indirect proof by citing specific logical…

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A: Given:(A→B) and (B →C) and not (A→C) First Change this statement into symbolic form:…

Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

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

Q: Deteimine the set of vectuns sci, iti), (1tiyzi)f linealy dependent or linenly Indefendteut? is

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Q: Verify the logical equivalence (p ^ q ^ ¬r) v (¬p ^ q ^ ¬r) = q ^ ¬r by using known logical…

A: Verify the logical equivalencep∧q∧¬r∨¬p∧q∧¬r≡q∧¬rby using known logical equivalences.

Q: The equivalence class of -1 for the relation congruence modulo 5 is O {...,-12, –7, –2, 3,8, 13,…

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Q: The contrapositive of “For all x, if x has property P then x has property Q” is

A: The contrapositive of “For all x, if x has property P then x has property Q” is

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Q: Explain the logic of a Kruskal–Wallis test.

A: Kruskal-Wallis test: The Kruskal-Wallis test is useful for comparing the means of the population…

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Q: Use the contrapositive to rewrite the statements in if-then form in two ways. Being divisible by 3…

A: Recall that “If P then Q” means “P is sufficient for Q” and “Q is necessary for P” to happen.…

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

A: Tautology lagical statement

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Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

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Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

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Q: Prove the equivalence using a truth table. 1. (p → q) → (~ p v q)

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Q: Prove that commutativity hol

A: Let x,y∈V and  x=(x1,x2,x3,......xn-1,xn)        &amp;       y=(y1,y2,y3,......yn-1,yn) Then we need…

Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Q: Let X = {a, b, c} and R={(c, b),(a, c)}. Then Check the all properties reflexive,symmetric,…

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Q: Let the statement be “If n is not an odd integer then the sum of n with some not odd number will not…

A: Proof by contrapositive: Let P and Q be two statements and if P is true then Q is also true. P → Q…