Question

Prove the following statement, please explain the steps,

m|n and n|m if and only if n = m or n = -m

Answer #1

Please prove the following statement, in FULL detail. (by the if
and only if proving technique, not induction!)
Prove that 5 | Un if and only if 5|n. Where Un is the Fibonacci
sequence.

Show all the steps and explain. Don't skip steps and please
clear hand written
f(x)=x^m sin(1/x^n) if
x is not equal 0 and f(x)=0 if x =0
(a) prove that when
m>1+n, then the derivative of f is continuous at 0
limit x to 0 x^n
sin(1/x^n) does not exist? but why??? please explain it should be
0*sin(1/x^n)

Let n be any integer, prove the following statement:
n3+ 1 is even if and only if n is odd.

Explain steps also please. Thanks.
- We want to implement "if (m != n) m--;" in LEGv8.
Suppose m and n are in X20 and X21, respectively. What should we
use in the blank in the following code segment?
SUB X9,X20,X21
_____ EXIT
SUBI X20,#1
EXIT:
- Suppose X20 contain the decimal value 5 and X21 contains the
decimal value -5. Which condition codes are set to 1 after the
following instruction is executed?
ADDS X9,X20,X21
- We want to...

Prove the following statement:
Suppose that (a, b),(c, d),(m, n),(pq,) ∈ S. If (a, b) ∼ (c, d)
and (m, n) ∼ (p, q) then (an + bm, bn) ∼ (cq + dp, pq).

Prove that a tree with n node has exactly n-1 edges. Please show
all steps. If it connects to Induction that works too.

Prove the following result. PLEASE EXPLAIN reasoning so I can
understand how to do it on my own.
Let x and y be integers. Then x ≡ y (mod m) and x ≡ y (mod n) if
and only if x ≡ y (mod L), where L = lcm[m, n]. Then expand to any
finite number of moduli

Prove the following statement: for any natural number n ∈ N, n 2
+ n + 3 is odd.

Prove the following statement by mathematical induction. For
every integer n ≥ 0, 2n <(n + 2)!
Proof (by mathematical induction): Let P(n) be the inequality 2n
< (n + 2)!.
We will show that P(n) is true for every integer n ≥ 0. Show
that P(0) is true: Before simplifying, the left-hand side of P(0)
is _______ and the right-hand side is ______ . The fact that the
statement is true can be deduced from that fact that 20...

Solve the following recurrences(not in Θ format) using backward
substitution. Please write all necessary steps.
M(n) = M(n - 1) - 3 where M(0) = 1,
M(n) = 2M(n-1) + 3 where M(0) = 3
M(n) = 4M(n-1) where M(1) = 2

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