(b) Decide whether the following are true or false giving a proof or coun- terexample as appropriate. (i) For all a, n, m ɛ Z. If a | n and a | m then a | (n + m). (ii) For all a, b, n, m E Z. If a | n and b| m then (a + b) | (n + m).

Q: 5. Prove the given statement. (a) If 4|x, then x² is even. (b) If x? +x + 1 is even, then x is odd.…

A: please see the next step for solution

Q: 3. Suppose that f(n) = 2f(n/2) + 3 when n is an even positive integer, and f(1) = 5. Find a) f(2) b)…

A:

Q: 5. a) Let X be Bin(6,0.7). Find P(X ≤ 5). Use the table. Bin(6,0.5) P(x <= 5) = Σ = 0.882 5 6…

A: The values of Binomial and Poisson distribution are given in the parts.

Q: Supposer FCE, acE is algebraic F and dog (a/F) 13 odd. Proveo that F(a)= F(a²). over

A:

Q: 12. Find x and m < A. Show ALL work to find x first. THEN find m< A. (7x-26) (5x-27) A (10x- 23)

A:

Q: 2. Suppose that f(n) = f(n/3) + 1 when n is a positive integer divisible by 3, and f(1) = 1. Find a)…

A:

Q: Solve 2|7-x| 8 c. -8 6

A: We have given the inequality; 2|7-x| &lt; 2

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: Let v = Find [-13]; ®= { [4]· [H] }; × = {[3]· B]}-· B C a. [v]: b. [v]: c. [B]: d. [B][v]: e. Are…

A: (.) Given,(.) Coordinate vector:  Let  be a basis of a vector space . Then coordinate vector of…

Q: 3. For n e N, we define n! = (n)(n – 1)(n – 2)... (2)(1). E.g., 4! = (4)(3)(2)(1) = 24. Prove the…

A: Here we have to prove two statements.

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

A:

Q: 2. (T/F) Given a predicate formula y, if we apply an "equivalence rule" to produce and equivalent…

A: A predicate formula φ is given and an "equivalence rule" is applied to produce an equivalent formula…

Q: (a) Show that if a > 0, then 1/a> 0 and 1/(1/a) = a. (b) Show that if a <b, then a < (a+b) < b.

A:

Q: b. {r|x € N and 7 <x< 14}

A: Given,  x|x∈ℕ and 7≤x≤14

Q: 7. Which of the following statements are tautologies? (Select all the choic that apply) (а) Р —Q (b)…

A: Introduction: When the truth value of a statement is always true, it is referred to as tautology.…