Prove the following: If m is an even number and n is an odd number, then n 2m is odd. Hint: start with the definition of an even number and the definition of an odd number.

Q: Prove the following statement by contradiction: There exist no INTEGER VALUES for A and B such that…

A: Proof by contradiction- Assume the negation of the conclusion and get the contradiction implies…

Q: what integer is closer to 6

A: given: the integer is six.

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: Determine which of the following integers are primes. a. 107 b. 111

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Q: Illustrate the following on a number line:a. |x|=4b. |x|c. |x|>4

A: Part a. For |x|=4 x =+4 and x=-4 are the two values of x on the number line.

Q: If a is an even number, then a³ is an even number.

A: Here, We have given that (a) is an even number then we have to prove that (a3)  is also an even…

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: Is the following proposition true or false? Justify your conclusion. n For each natural number n, 3…

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Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: A number is very close to zero. Another number is also very close to zero. The quotient, , therefore…

A: Given a number is very close to zero. Another number is also very close to zero. Let α>0 is very…

Q: Suppose that E and F are points on the number line. If EF = 13 and E lies at -5, where could F be…

A: Suppose that E and F are points on the number line. If EF = 13 and E lies at -5, where could F be…

Q: Mean of two numbers 5 and 7 is____ ?

A: Given: Two numbers are 5 and 7.

Q: .Prove that if n is an odd number then 3n + 1 is an even number. Use direct proof. 2.Prove that…

A: Given n is odd number

Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

Q: The S.D. of the first n odd integers is √85 , find n

A: Sum of first n odd numbers is given by: ∑ixi=n2 Sum squares of first n odd numbers is given by:…

Q: Which statement is true for the values of P and Q on this number line? + -5 -4 -2 F1 1 A (B) PxQ 4…

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Q: 2 ) + ("**) = n²- .2 2

A: