Suppose f: integer(z) to integer(z) is a function with the property that f(a+b) = f(a) + f(b) for every two integers a and b. Prove that if f(c) is even for some odd integer c then f(x) is...

Suppose f: integer(z) to integer(z) is a function with the property that f(a+b) = f(a) + f(b) for every two integers a and b. Prove that if f(c) is even for some odd integer c then f(x) is...

Suppose f: integer(z) to integer(z) is a function with the property that f(a+b) = f(a) + f(b) for every two integers a and b. Prove that if f(c) is even for some odd integer c then f(x) is...

Deﬁne f(x) : P({a,b,c}) →N as follows: for all A ∈P({a,b,c}), f(A) = the number of elements in A. ( P is a power set.) Is f one-to-one? Prove or give a counterexample. Is f onto? Prove...

discrete mathematic

For all positive integers m and n, with m<n if m divides (35n) then either m divides 35 or m divides n

I need help

1. Define the following predicates: [6] R(x) : “x is a right angle triangle.” O(x) : “x has an obtuse angle.” Now consider the following statments: S = ¬∃x(R(x) ∧ O(x)) T...

4, 12, 20, 28, 36, 44, 52, 60 f(n) =___ans________

The following problem consists of an assertion and a ‘proof’. Identify any error(s) in the ‘proof’. If there are errors but the assertion is true, provide a correct proof. Otherwise, provide a counter-example...

Q(n) = {0 ...

Determine all elements A={1+1(-n)2/ n E n}

prime numbers a={xEz+//x+2<5-} determine all elements

Prove the statement is true using mathematical induction: 2n-1 ≤ n!

Every year, Alice gets a raise of $3,000 plus 6% of her previous year's salary. Her starting salary is $20,000. Give a recurrence relation for S(n), Alice's salary after n years, for n ≥ 0. S(n)...

Create a logic circuit for the logical proposition P∨Q∧¬P

1. How many different positive integers can be made from the digits {2, 4, 6, 8} if repetitions are allowed? 2. What is the telescoping form of f(x) = x4 + 7x3 - x2 + 2x +...

I am wondering if this is correct. Proof: Suppose f: X - > Y and g: Y -> Z are functions such that g is onto. Let z ∈ Z. Since, g o f is onto, there exists x ∈ X such that g o...

The Fibonacci sequence F0, F1, F2, F3, ... is an infinite sequence defined by the two initial values F0 =0, F1 =1, and the rule Fk = Fk-2 + Fk-1 for all k ≥ 2. Let Μ...

5.:Let f: X →Y be a function.True or False?A sufficient condition for f to be one-to-one is that for all elements y in Ym there is at most one x in X with f(x)= y.

The Fibonacci sequence F0, F1, F2, F3, ... is an infinite sequence defined by the two initial values F0 =0, F1 =1, and the rule Fk = Fk-2 + Fk-1 for all k ≥ 2. Let Μ = [1 1 ...