Consider the following axioms: [1] Every child loves Santa. [2] Everyone who loves Santa loves any reindeer. [3] Rudolph is a reindeer, and Rudolph has a red nose. [4] Anything which has a red nose is weird or is a clown. [5] No reindeer is a clown. [6] Scrooge does not love anything which is weird. Questions : Convert the above axioms into FOL and Prove by resolution that “Scrooge is not a child”!

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: Complete the following proof. Given: FG FJ, HG = IJ Prove: HF = IF

A: I have provided solution in step2.

Q: 4. Complete the following proof in the format of your choice. D. 3. Given: AB DC and AB || DC Prove:…

A:

Q: 12. What can you conclude from (PV Q) ^ ¬P? Prove it.

A:

Q: If a+a e c(R) for all ae R. then Commutative is prove that

A:

Q: Let n E Z. Prove that if 3/ (2n² + 1), then 3 | r n.

A: Solution:     Let 3 does not divide n      => n = 3k ± 1 for some integer k.       => 2n2 + 1…

Q: If k >= 2 and x in R^ k prove that there exists y in R^ k such that y ne0 but xy = 0 Is this also…

A: If x has any components equal to 0, then y can be taken to have the corresponding components. equal…

Q: 1. Prove that the followingn is a theorem in SD. Av - A

A: Theorem :-

Q: 6. Prove that if alb and k E Z, then a|(b+ ak).

A:

Q: Let AB = AC. Prove that if det(A) = 0, then B = C.

A: The given question Let AB = AC. Prove that if det(A) = 0, then B = C. this question is not correct…

Q: Complete this following proof in its proper format:   Proof= { (∀x)(∀y)(Rxy->Rxy), (∀x)Rxb } |-…

A: The given statement is  ∀x∀yRxy→Rxy,∀xRxb|-∀xRbx. we have to prove the statement in the following…

Q: Give a natural deduction proof of ¬(A V B) from hypothesis ¬A A¬B.

A: Please find the answer in next step

Q: Let fca) satis fies Cauchy Riemann Eguation , then (f(z)" is also satis fies cauchy Riemann Eguation…

A:

Q: - Justify the last two steps of the proof. Given: RS UT and RT US Prove: ARST AUTS

A: Given that:

Q: Construct a Fitch proof of the following theorem: Suppose p V q, and suppose r. Then p V (q r).

A: Given that - p V q, and supposer r.

Q: HeW. By the Same way Prove that: X Ju (x) (X)

A:

Q: - Find a bijection between Z and E (the even numbers), prove your answer is correct.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Suppose m e Z. Prove by both contrapositive and contradiction that if m² + 2m + 4 is odd, then m is…

A:

Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y>9⇒x>54∨y>49, where x, y∈ℝ. Prove the statement using method of…

Q: Provide a left-hand-side, right-hand-side proof of the following: dt

A:

Q: 7. Consider the figure to below. Which of the following statements are correct? Select all that…

A:

Q: - Prove the following: gcd(m,n) = 1 + 3x, y E Z such that mx + ny = 1. One direction can be done by…

A: We will prove this by using some properties of division. One way will be done with the help of…

Q: 3. Use the above Lemma and Mathematical Induction to generalize the previous exercise. That is,…

A:

Q: 4. Complete the following proof in the format of your choice. D 3. Given: AB a DC and AB || DC…

A: Given figure, Given : AB¯ ≅ DC¯  and  AB¯ ∥ DC¯ we have to prove ∆CAB≅∆ACD

Q: Let AB = AC. Prove that if det(A) + 0, then B = C.

A: Given: Let AB=AC. To Prove: If detA≠0, then B=C

Q: II. Prove the following. 1. alb iff ac bc, where c + 0.

A:

Q: 7. Prove: Vn e Z, n is odd if and only if n is odd.

A:

Q: If x is a lower bound for S in R, then x must be unique. a. True b. c. Never True Sometimes True

A: We want to find the given statement is true of false.

Q: 3. Let n E Z. Give a direct proof that there exist x, y E Z such that n = 55x + 78y.

A: Objective : To prove for any n∈ℤ ∃x,y∈ℤ such that n=55x+78y Prove for n=1, Greatest common divisor…

Q: discrete

A: In method of contradiction we start by assuming that given statement is false. Then prove that it is…

Q: Prove: Provided it exists, (A-1)¯ = A.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Let -{[:);}--{:)[:} -{{)}} Both B and C are bases for R2. If {x}s =: -[:], what is {x}c?

A:

Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

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Q: 2) Let a,bE Q such that a<6. Prove that ax <bx.

A: The statements can be proved by analyzing the results from the given statements. The other methods…

Q: Prove the following existence proof. P: 3a, y, z E N such that ryz = 24

A: Existence proof

Q: Prove the given statement by the indicated method. (1). By Direct Proof: "Vm,n € Z*,+> 2."

A: ∀m, n∈ℤ+,We know square of an integer is always non-negative Hence (m-n)2≥0…

Q: Indicate the method you would use to prove the two A's .If no method applies, enter "none". O SSS…

A: We have to show congruent of triangle

Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

A:

Q: Prove or disprove the following: Vne Z, n³ + n²+1 is odd

A:

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: Give a direct proof of the claim: Vn E N, if the last two digits of n are divisible by 4 then n is…

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Q: (e) The proof of Theorem 1 is thus currently incomplete, as it does not explicitly use the…

A:

Q: 14. Given: AB | DC; AB = CD; 21 = L2 To prove that DE = BF, what would you prove first? a. AADE =…

A: Given: AB∥DC¯; AB≅DC¯; ∠1≅∠2

Q: Prove: Vn e Z,if n is odd, then 3n+5 is even.

A: Consider the provided question, To prove: if n is odd integer, then 3n + 5 is even. Proof by…

Q: Prove the following using resolution refutation: 4. Given: (p Aq) -→r, p^ s A~w, (s A t) →q, tv w…

A: Given 4 premises p∧q→r, p∧s∧~w, s∧t→q, t∨w. The conclusion to be proved is r. We know that a…

Q: Q.No.6. Prove that by mathematically Induction 2" 2.

A: Let Pn: 2n&lt;n+1! For n=2 LHS is 22=4 and RHS is 2+1!=3!=6 As 4&lt;6 So, Pn is true for n=2 Let the…

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: 3.1 Prove: For all a and B in R, Ja + B] > | |a| – |B||. Hint: la + B] = |a – (-B)|-

A: Answer is in below steps.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.