Question

Use a proof by cases to show that:

**min(a, min(b,c)) = min(min(a,b),c),** whenever
**a, b, and c are real numbers.**

**min(a,b) = a,** if **a ≤ b**...
**min (a,b) = b** otherwise.

Answer #1

Consider the statement that min(a, min(b,
c)) = min(min(a, b), c)
whenever a, b, and c are real
numbers.
Identify the set of cases that are required to prove the given
statement using proof by cases.
Multiple Choice. Choose correct one.
a ≤ b ≤ c, a ≤ c ≤ b, b ≤ a ≤ c, b ≤ c ≤ a, c ≤ a ≤ b, c ≤ b ≤
a
a>b>c, a>c>b, b>a>c, b>c>a, c>a>b,
c>b>a.a>b>c, a>c>b, b>a>c, b>c>a,...

****Please show me 2 cases for the proof, one is using
n=1, another one is n=2, otherwise, you answer will be thumbs
down****Hint: triangle inequality. Don't copy the online answer
because the question is a little bit different
use induction prove that for any n real numbers, |x1+...+xn|
<= |x1|+...+|xn|.
Case1: show me to use n=1 to prove it, because all the
online solutions are using n=2
Case2: show me to use n=2 to prove it as well.

Use proof by contradiction to prove the statement given. If a
and b are real numbers and 1 < a < b, then
a-1>b-1.

discrete math (3) with full proof
Use the Well Ordering principle to show that a set S of positive
integers includes 1 and which includes n+ 1, whenever it includes
n, includes every positive integer.

1. Give a direct proof that the product of two odd integers is
odd.
2. Give an indirect proof that if 2n 3 + 3n + 4 is odd, then n
is odd.
3. Give a proof by contradiction that if 2n 3 + 3n + 4 is odd,
then n is odd. Hint: Your proofs for problems 2 and 3 should be
different even though your proving the same theorem.
4. Give a counter example to the proposition: Every...

Proof by contradiction: Suppose a right triangle has side
lengths a, b, c that are natural numbers. Prove that at least one
of a, b, or c must be even. (Hint: Use Pythagorean Theorem)

DISCRETE MATHEMATICS PROOF PROBLEMS
1. Use a proof by induction to show that, −(16 − 11?) is a
positive number that is divisible by 5 when ? ≥ 2.
2.Prove (using a formal proof technique) that any sequence that
begins with the first four integers 12, 6, 4, 3 is neither
arithmetic, nor geometric.

Please show the proof that:
Either [a]=[b]
or [a] *union* [b] = empty set
this will be proof by contrapositibe but please show work:
theorem: suppose R is an equivalence of a non-empty set A. let
a,b be within A
then [a] does not equal [b] implies that [a] *intersection*
[b] = empty set

Show that if a, b, c are real numbers such that b > (1/3)a^2
, then the cubic equation x^3 + ax^2 + bx + c = 0 has precisely one
real root

Give both a direct proof and an indirect proof of the statement,
“If A ⊆ B, then A\(B\C) ⊆ C.”
[Both Show-lines and a ﬁnal presentation are required.]

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