Prove the following statements. b. Let a, b EZ, then ab is odd if and only if both a and b are odd. c. Let a, b € Z. If a² + b² is odd then ab is even. d. Let a, b e Z. The sum a+bis even if and only if a and b have the same parity. e. Let a, b € Z, then a + b and a - b have the same parity.

Q: 6. Let A= {1,3,5), B = {2,4,6,8), C={2,3,4,5) Which of the following statements is false? A. An B=0…

A: We have to check which of the following statements is false.

Q: Q: If a,,a,, aza,. are in A.P. such that a, +a, + ao + as + az0 +a24 = 450 Then find the sum a, + az…

A: Given: a1, a2, a3, a4, .....  are in A.P.  such that:a1+a3+a10+a15+a20+a24=450

Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

A: Note: As per Bartleby guidelines if a question have more than 3 subparts and specific part is not…

Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: = [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the…

A:

Q: Q. be the sum of the digits of your registration_number, (e.g. 3BA-abc, S i+b+č). Assume that the…

A: Given data is,

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

A: We will disprove the given statement by giving a counter example that is we will give values for a…

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

A:

Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: Given A and B = [6 –7 -1 8], find AB and BA . | -2 АВ BA : ||

A:

Q: Let a, b, and c be natural numbers. Prove a ∙ (b + c) = a ∙b + a ∙ c.

A:

Q: a. Let a Z, then a² - 5a +7 is odd.

A:

Q: | − x + 2| − 3 ≤4

A: Given  -x+2-3 ≤ 4 We have to find the values of x.

Q: Which statement is an example of a transitive relationship? If x = 2y and 2y = 8, then x = 4. If clm…

A: Transitive relationship is a relationship in which if from the first two condition 3rd condition can…

Q: let a and b be integers. Show: if a * b is odd, then a is odd and b is odd

A: A number is even, if it is divisible by 2. A number is odd, if it is not divisible by 2. The odd…

Q: 18. Show that P→ qand-q→→p are logically equivalent.

A: We have to show that  and  are logically equivalent.

Q: If a1, az, az,.-ans. be the A.P. and S, = a-1m+1+a-1m+2+a-1n+3 +.--+ am %3D Prove that :…

A: In this question we have to proof S1, S2, S3,.... are in Arithmetic Progression.

Q: d = (a, b, c).

A:

Q: Challenge. Establish the Cauchy-Schwartz inequality: For real numbers we have (a + az + ..+ a) (b+…

A: Prove the Cauchy-Schwartz inequality…

Q: Q2: if A= [{1,2},{3}], H= [{1}, {2,3}], G= [{1,3}, {2}] Show that A, H and G are mutually disjoint

A: Note: " Since you have posted multiple questions. we will solve the first question for you. To get…

Q: Recall that each permutation can be written as a product of disjoint cycles. How many permutations…

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Q: 1. The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is the largest number that…

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Q: Suppose that P(A) = 0.4, P(B) = 0.3 and PAUB)-042, then a. A and B are dependent b. none of the…

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Q: 9. Classify each of the following statements as true or false, for all whole numbers a, b, and c,…

A: ?Two integer a|b ( a divides b) means there exists an integer k such that       b= a×k . ?Product,…

Q: If |A|  8 and |B|  5, what is |A ∪ B| + |A ∩ B| ?

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Q: Let |4|= 3m and B|= 4 , then |4 B| is m=3.6 إجابتك

A: Given that |A|=3m and |B|=4 find A-1B also m=3.6