Question

) Prove or disprove the statements: (a) If x is a real number such that |x + 2| + |x| ≤ 1, then |x ^2 + 2x − 1| ≤ 2. (b) If x is a real number such that |x + 2| + |x| ≤ 2, then |x^ 2 + 2x − 1| ≤ 2. (c) If x is a real number such that |x + 2| + |x| ≤ 3, then |x ^2 + 2x − 1 | ≤ 2. (d) If x is a real number such that |x + 2| + |x| ≤ 5, then | x ^2 + 2x − 1 ≤ 2.|

Answer #1

Discreet Math: Prove or disprove each statement
a) For any real number x, the floor of 2x = 2 the floor of x
b) For any real number x, the floor of the ceiling of x = the
ceiling of x
c) For any real numbers x and y, the ceiling of x and the
ceiling of y = the ceiling of xy

Here are two statements about positive real numbers. Prove or
disprove each of the statements
∀x, ∃y with the property that xy < y2
∃x such that ∀y, xy < y2 .

Prove or disprove the following statements. Remember to disprove
a statement you have to show that the statement is false.
Equivalently, you can prove that the negation of the statement is
true. Clearly state it, if a statement is True or False. In your
proof, you can use ”obvious facts” and simple theorems that we have
proved previously in lecture.
(a) For all real numbers x and y, “if x and y are irrational,
then x+y is irrational”.
(b) For...

Prove or disprove the following statements.
a) ∀a, b ∈ N, if ∃x, y ∈ Z and ∃k ∈ N such that ax + by = k,
then gcd(a, b) = k
b) ∀a, b ∈ Z, if 3 | (a 2 + b 2 ), then 3 | a and 3 | b.

Prove or disprove:
If 2x ≡ 6 mod10, then x ≡ 3 mod10.

When we say Prove or disprove the
following statements, “Prove” means you show the
statement is true proving the correct statement using at most 3
lines or referring to a textbook theorem.
“Disprove” means you show a statement is wrong by
giving a counterexample why that is not true).
Are the following statements true or not? Prove or disprove
these one by one. Show how the random variable X looks in each
case.
(a) E[X] < 0 for some random...

5. Prove or disprove the following statements:
(a) Let R be a relation on the set Z of integers such that xRy
if and only if xy ≥ 1. Then, R is irreflexive.
(b) Let R be a relation on the set Z of integers such that xRy
if and only if x = y + 1 or x = y − 1. Then, R is irreflexive.
(c) Let R and S be reflexive relations on a set A. Then,...

Prove or disprove: If a real 5x5 matrix has a non-real
eigenvalue, then it has 5 distinct eigenvalues.

Prove the statement
For all real numbers x, if x − ⌊x⌋ < 1/2 then ⌊2x⌋ =
2⌊x⌋.

1. Let x be a real number, and x > 1. Prove 1 < sqrt(x)
and sqrt(x) < x.
2. If x is an integer divisible by 4, and y is an integer that
is not, prove x + y is not divisible by 4.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 9 minutes ago

asked 22 minutes ago

asked 27 minutes ago

asked 28 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 35 minutes ago

asked 43 minutes ago

asked 1 hour ago