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Discrete Math : Logic (40 MC Problems)
It uses concrete examples as a means of proof by cases.
d. It is widely accepted as valid.
14. 2 | (n2 + 3n) for all n ≥ 1. (Hint: Use mathematical induction.)
a. True
b. False
15. 2n + 3 8804; 2n for all n ≥ 4.
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Many problems on group theory
Identify the identity element for +; in addition, for each n in Z, identify the inverse. Also show that + is associative.
- If (R, à?) is a group, show that it is.
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Partial order relation
( a, b, c ) R ( d, e, f ) <-> a 8804; d, b 8804; e, c 8804; f,
where 8804; denotes the usual "less than or equal to" relation for real numbers. Do the maximal, greatest, minimal and least elements exist? If so, which are they?
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Inequality for convex function
Define
F(s,t) = f (s) + f(t) - 2f((s+t)/2)
Prove that F(s,t) 8804; F(a,b) for every s,t ∈[a,b]. Please see attachment.
Proof. First, we observe that for each s, t (please see the attached file) [a,b] we have that F(s, t) = F(t, s).
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Associative and Commutative Rule
each way requires a definition or two:
1) for n≥2, 08804;a, b8804;n+1
a+n(written as a power in a corner downside, but dont know how to put it tho) b={condition 1 - a+b if a+ba+n-n if a+b>or=n}
2) writing an(n is written
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Derivatives and Differential Equations and Leaking Tank Word Problem
(b) How many gallons of water are in the tank at time t = 3 minutes?
(c) Write an expression for A(r), the total number of gallons of water in the tank at tune r.
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Commutative Rings, Ideals, Kernels, Matrices and Injective and Surjective Ring Homomorphisms
e) Show that R ={[a 0]|a,b,c Є R} is a subring of M2(R). Is it commutative? Find a non trivial ideal of R.
[b c]
f) Is S ={[a b]|a,b,c Є R} is a subring of M2(R)?
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Joint and Marginal PDFs of Points in a Rectangle
94886 Joint and Marginal PDFs of Points in a Rectangle 9. Suppose that a point (X, Y) is chosen at random from the rectangle S = {(x, y) 0 8804; r 8804; 2 and 1 8804; y 8804; 4}.
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Quantitative method :MCQ
A) 2 R + 4 D ≥ 480
B) 2 D + 4 R 8804; 480
C) 2 R + 3 D 8804; 480
D) 2 R + 4 D 8804; 480
E) 3 R + 2 D 8804; 480
TRUE/FALSE.
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Cauchy's Formula
37957 Cauchy's Formula Use Cauchy's formula for the derivative to prove that if f is entire and
|f(z)|8804; A|z|² + B|z| + C for all zεC,
then f(z) = az² +bz + c
Please see attached for full