2. Suppose a, b, and care integers. Prove that if a |band alethen a |b+c and a|b-c.

Q: Show that if a|b then -a|b.

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Q: (e) Either the plant at site 1 or both of the other plants are completed by the contract date. O A,…

A: It ia asked that either the plants at site 1 or both of the other plants are completed by the…

Q: Let M = {14*: kEZ*} and A = {7k:k € Z*}. Then

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Q: Hamilton circuit

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Q: Show that if a and b are positive integers, then there are divisors c of a and d of b with (c, d) =…

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Q: If ∠A≡∠C in ABCD, then ABCD is cyclic.

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Q: 2 Let A | and U = H. Then A2017U is equal to = ... A) B

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Q: Suppose there were 600 nurses graduating this year.  Assume that 400 were registered nurses (RN),…

A: Need to complete venn diagram

Q: An element x is in A ∪ B if, and only if, _____________________.

A: Known fact: A∪B=x | x∈A or x∈B

Q: Show that if A ⊂ B, then C – B ⊂ C – A.

A:

Q: If "C, = K "C,, then K is n-1 %3D

A: Combination problem....

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: If D =diag(λ1,λ2,...,λn), show that for every positive integer k, Dk =diag(λk 1,λk 2,...,λk n).

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Q: In ([0, о), т оос), if A %3DN, then A'%- Оа. А-{1} O b. [0,0) О с. (0, о) O d. Ø О е. А

A: ( [0, infinity) , Tcoc)  Since it is Co-countable topology. All countable sets are closed in given…

Q: d, thenab d | | m and b m. Show that if gcd(a, b) Let a and b be nonzero integers with a m.

A: To prove the required divisibility property under the given conditions

Q: Prove that at a party where there are at least two people, there are two people w know the same…

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: Prove that if A – B – D and B – C – D, then A -C– D.

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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: . Prove the following: If gcd(a, b) = 1 and ca then gcd(b, c) = 1

A: We will prove the given statement.

Q: a. Suppose that Natasha, Monim and Rehan a

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

Q: If m, n, p, q are integers, n > 0, q > 0, and r = m/n = p/q, prove that

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Q: 22. If 6log2x =18 , then x is

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Q: Prove that If k, q, w and r are integers, and if c|k and c|q, then c|(kw + qr)

A: We know that  Definition of Divisibility : If a and b are integers such that a≠0, then we say "a…

Q: Prove by contradiction that if m, n € Z, then m² - n is even or m-n-1 is even.

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Q: Suppose a, b, c, d e Z, a + b = c, and dla. Prove that d|b if and only if d|c. 5.

A: see below the calculation steps

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

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Q: If a is transcedental over Q then a^2 is also transcedental over Q

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Q: v 26. Show that if a < c < b, then C-a b favg [a, b] = b favg [a, c] + b favg [C, b] a |

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Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

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Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: If a, b, and c are integers such that b is a multiple of a and e is a multiple of b², then c is a…

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Q: - Show that (for n = 0, 1, 2, ..) (a) F(-n, b; c; 1) = - (c-b)n (c)n

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Disprove: For all integers a,band c, if a|(bc) then a|b and a|c

A:

Q: Suppose A, Band C are finite sets of integers. Decide whether each of the following is a set, a…

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Q: Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09, what…

A: Given Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09

Q: 32, as 185, and a6 = 1121. Find a1, a2, 5an-1+ 6an-2+ lan-3 and a4 Suppose an and a3-

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Q: 1. Given a deck of 30 cards labelled with numbers 1- 10 (with 3 cards of each number), how many…

A: From the given information,  A deck of 30 cards labelled with numbers 1-10 (with 3 cards of each…

Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

A:

Q: (а-b) a (b-c)* 3 d

A: a, b, c, d are in continued proportion Therefore, we have ab = bc = cd = k (say) c=dk, b=ck=dk2,…

Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

Q: Suppose we randomly select a subset of positive integers. How large must the subset be, if we want…

A: The Pigeonhole Principle:  If there are p+1 or more pigeons, need to distribute among p pigeonholes,…

Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Q: elsewhere. ind (a) K (b) CDF of X

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Q: Compute (x – 2) for the following set of n = 7 values. X1 = 8, x, = 15, x3 = 14, x4 = 10, x5 12, x6…

A: Given,   =?

Q: Show that 1 (N, <) is well-ordered. 1 2 (Z, <) is not well-ordered. 3 (R, <) is not well-ordered.

A: Please send questions as different questions. We cannot do more than 3 at a time.   A relation ≤ on…

Q: If A subut of B. where B 18 a closo d subset of IR show that

A: Given: A is a subset of B, where B is closed subset of ℝp. To show: A¯⊆B.