Prove or Disprove: Va, b, c E N, if a | bc and c| ab then b lac. (Here | denotes divides.)

Q: ove that if AB = 1, then B = A- 2, 1 -1 21 and (b) 3 1 1 1 -2 1 2.

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

Q: Which statement is true? A) All similar figures are congruent. B) All congruent figures are similar.…

A: we have to select one

Q: 3. 16 |15 13 14 o2 57 618 9/10 d 112

A:

Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: The question is Prove or disprove: for all integers a, b, c, d, if a divides both b − 2c and c − d,…

A:

Q: Prove the statement; a – c is a divisor of ab + cd=→a – c is a divisor of ad + bc.

A: We need to prove the statement; a – c is a divisor of ab + cd => a – c is a divisor of ad + bc.

Q: coprime

A:

Q: If a, bEZ such that a b then the numbers a and b are called relatively prime numbers if ged (a, b)…

A: True

Q: Statement Reason PN bisects ZMNO Given: PN bisects ZMNO MN ON MN = ON ZMNP ZONP NP NP Prove: AMNP =…

A:

Q: determine which of the followingmatrices are nonsingular:

A: Given, 1322141-72 We say that a matrix is singular if its determinant is zero otherwise we say it is…

Q: Z Let AABC and ADEF have corresponding pairs of sides which are parallel. Say, AB || DE,BC || EF, AC…

A: given triangles are    △ABC  and   △DEF Also,       AB||DE,   BC||EF,   AC||DF yes it follows that…

Q: Let R be the set of all real numbers. Is R*, R , {0}} a partition of R? Why or why not? Select- v.…

A:

Q: 21. Lines / and m are cut by transversal n. Which statement would prove / || m. m22 = m26 m 22 = m3…

A:

Q: For all intergers a,if 6|5a,then6|a. Prove or disprove this statement."|"means divides

A:

Q: 5. Which is a counterexample that shows that, for whole numbers a and b, a ÷b = b÷ a is false? O a =…

A:

Q: Chow that ॥२ + १n + 3 (nt) (2nt3)(2nt5) (nt 4) 36

A:

Q: For all integers a, b and c, if a|b and a|c, then a|(b^2-c^2)

A: Division

Q: Prove that if n divides a, b, and c, then n³ divides a²(b – c) + b² (a – c) +²(b – a).

A: A product is a multiplication of two or more terms and these terms are called the factors of the…

Q: Prove by, Proof by Contrapositive.   (a) Suppose x ∈ Z. If x2− 6x + 5 is even, then x is odd.   (b)…

A: In the question it is asked to proof the following  If x2− 6x + 5 is even, then x is odd If 5 |x y,…

Q: Need a formal proof: Show: Let x,y ∈ R. Then | |y| - |x| | ≤ |y-x|. Hint:a = |x|, b=|y| and ε =…

A:

Q: 1. Use a two-column proof to prove the equivalence below -(P V-Q) v (-PA-Q) = ¬P

A: We will use basic equivalence laws of logic

Q: Do values exist for p, q, r such that the compound expression is satisfiable? (pAqAr)V(¬qA¬r)?

A:

Q: PvQv R= (~P = Q)v (~P = R)

A:

Q: 8. Which lines, if any, can be proved parallel given the following diagram? Provide the…

A: Diagram :

Q: Prove the suggested proofs by filling In the missing blanks. Given GC 1 PS and G5 1 CF Prowe: AGCS…

A: According to question given that∆∆GCS≅∆PSC

Q: Prove the following are valid (theorems) using resolution: (You must negate!) 1) (~Q->~P)--> (…

A: As per norms, we will be answering only the first question. If you need an answer to others then…

Q: (7) For any nonzero a, b € Z, the gcd(a, b) divides the lem(a, b). (8) If r, y € Z and 3 divides ry,…

A:

Q: The statement "If mLA = mLB and m LD = m LA + m LC, then m LD = mLB + m LC" is justified by what…

A: Given statement is "If m∠A=m∠B and m∠D=m∠A+m∠C then m∠D=m∠B+m∠C. To find the property which justify…

Q: 2. Find Ju x v| and determine whether u x v is directed into the page or out of the page. |v|= 5 45°…

A:

Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

A:

Q: 10. Write a two-column proof: Given: a // b, Prove: 21 is supplementary to 23 2, Statements Reasons

A:

Q: 8. EXTRA CREDIT A Given: AB 1 BC, dC I BC, AC DB Prove: AB 2 DC C STATEMENT REASON

A: Solution of this question is

Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

A:

Q: 10. Show that there is a distributive law also for difference: (A\ B)nC = (AnC) \ (BnC). Is the dual…

A: We need to prove the distributive law for differences and also check whether it is true for dual as…

Q: 11. Write a two column proof. Given: NP = OM, MN = PO Prove: ANMP=NOPM N M P

A:

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

A:

Q: Prove by contrapositive: For all integers a,b and c, if a [ bc then a [ b. (J means does not divide)

A:

Q: Prove rem (a+b,c) = [rem(a,c) + rem(b,c)] , c

A: Note: rema,b=the remainder when a is divided by b. Then, by the quotient remainder theorem, there…

Q: For "x is in the symmetric difference of A and B" give an equivalent statement that uses "x is in A"…

A:

Q: 1. Which property of equality allows you to conclude that the following is true? If mZD mE and mZE…

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

Q: Prove. 'if 0 < a ≤ b, then a2 ≤ b2 and √a ≤ √b.'

A: According to question,Given condition,0&lt;a≤b

Q: 2. Which of the following statements is true? Prove or give a counter example. d. An(B\ C) = (An…

A: (d) To prove that                   A∩B \ C =A∩B \ A∩C

Q: Determine OK. (where the intersection is taken over all nEN) if K, =[ -2+

A: Kn=[-2+1n,1en)

Q: Prove the inequality b−ab≤lnba≤b−aa provided 0&lt;a≤b.

A:

Q: prove that if a>4 then (a-2)^2>4

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.