Prove or disprove each of the following statements.
(a) There exists a prime number x such that x + 16 and x + 32
are also prime numbers.
(b) ∀a, b, c, m ∈ Z +, if a ≡ b (mod m), then c a ≡ c b (mod
m).
(c) For any positive odd integer n, 3|n or n 2 ≡ 1 (mod 12).
(d) There exist 100 consecutive composite integers.
Let {an} be a bounded sequence. In this question,
you will prove that there exists a convergent subsequence.
Define a crest of the sequence to be a
term am that is greater than all subsequent terms. That is,
am > an for all n > m
(a) Suppose {an} has infinitely many crests. Prove
that the crests form a convergent subsequence.
(b) Suppose {an} has only finitely many crests. Let
an1 be a term with no subsequent crests. Construct a...
If a business can prove that a ________________ exists, then
they can legally discriminate on the basis of membership in a
protected class.
Group of answer choices F
-FMLA.
-BFOQ.
-Burden of proof.
-Either A or B above.
a. Prove that for any vector space, if an inverse exists, then
it must be unique.
b. Prove that the additive inverse of the additive inverse will
be the original vector.
c. Prove that the only way for the magnitude of a vector to be
zero is if in fact the vector is the zero vector.
If a negative externality exists, then there is a __________
when society produces the market output instead of the socially
optimal output. This exists because the __________ to sellers and
third parties are __________ the __________ derived by buyers.
a. net social benefit; costs; greater than; benefits
b. net social cost; benefits; less than; costs
c. net social cost; costs; greater than; benefits
d. net social cost; costs; less than; benefits
e. none of the above
Prove that there exists integers m and n such that 15m + 12n =
3
Please do not prove by assuming m=1 and n=-1, I'd like to prove
by not assuming any actual numbers.
Let t be a positive integer. Prove that, if there exists a
Steiner triple system of index 1 having v varieties, then there
exists a Steiner triple system having v^t varieties
Demonstrating that a correlation exists does not prove that
changes in one variable are the cause of changes in the other,
partly because other factors which are undetected may be
influencing both known variables. Thus, knowing that a correlation
exists may lead to two or more different interpretations of the
correlation. For each of the studies described below, decide
whether the correlation is positive or negative and give two
explanations for the finding.
1 A government study reveals that the...