Let & € N. Prove by using the contra-positive that if ³ is odd then is odd. Proof: Choose which of the following statements supports this premise: [Select] [Select] x=2a implies x^3=8a^3=2(4a^3) x=a implies x^3=a^3 x=3a implics x^3-27a^3-3(9a^3)

Q: Prachice Let a^Nerp) and 9nG6) be cindap cndant. Shaw that 7u^NB(t !,p).

A: Negative Binomial Distribution: If we have a sequence of trials each having two outcomes, say…

Q: Which of the following statement is true in ZZ? O O O (0=1+x)^AXE (0=A+X)^EXA (0=1+x)^AXA None of…

A: We want to find true statement.

Q: for x belonging to Z,  prove or disprove 2x^2 +x +1 must have a remainder 1, 4, or 5 when divided by…

A: Given statement is false

Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: Prove that there is a positive number z so that z^5 + 10z = 10.

A: TO PROVE:-  There is a positive number z satisfying z5+10z=10 GIVEN :- z5+10z=10

Q: (a) (2x*y')(-x*y) (b) (2х- Зу)(3х - у) 4.(a)_ 4.(b)_ 4.(c)_ 4.(d) (e) (x-y)(x² + xy+ y°) OHER 4.(e)_

A: As we know from the exponent rule; 1). am·an=am+n 2). aman=am-n   (a). Given: 2x4y3-x5y

Q: n>=0

A: According to the question,    False. This statement is not true for all integers n >= 0. A…

Q: for the discrimanat here dont we do (Uxy)^2-(Uxx*Uyy)

A: Please see the below picture for detailed solution.

Q: Suppose a is an integer. Prove that if a^3 is a multiple of 3, then a is a multiple of 3.

A: Let a3 is a multiple of 3 but a is not a multiple of 3.a3 is a multiple of 3Therfore, 3 divides…

Q: True or false: If a,b,m are integers with m > 0 satisfying m|(a^2 − b^2), then m |(a −b). Justify…

A: Given Information: If a,b, and m are integers satisfying m|a2-b2. To check: m |(a −b) for any…

Q: Prove the claim that there are no integers j and k such that j^2 + 3k^2 = 8

A: Since both j and k are being squared so if we prove the case for positive integers, that will prove…

Q: Suppose that 2^n − 1 is prime. Show that n must also be prime. (Hint: try to find a convenient…

A: Given that 2n-1 is prime. To prove that n must also be prime. On the contrary let us assume that n…

Q: Suppose the following theorem is proven using a direct proof. Theorem: If x is a real number and x…

A:

Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

A:

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: By considering uniqueness of factorization of integers, find all pairs (x, y) ∈ N^2 such that x^2 −…

A:

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A: