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Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
Author: Gilbert, Linda, Jimmie
Publisher: Cengage Learning,
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
Transcribed Image Text:(a)
(b)
Let X
==
{5, {5,6}}. How many elements does the set X have? Give
the power set P(X).
Prove that the sets
x-5
A = {x Є Z:
6
€ Z} and B = {3k: k Є N}
are disjoint, i.e. AnB = 0.
(c)
(d)
(e)
Prove by induction that for all natural N,
N
Σ k (k + 1) = ½ N(N + 1)(N +2).
k=1
Indicate clearly where you use the inductive hypothesis.
Use proof by contradiction to show that 2 is irrational.
Write the number 6.29474747474... as an infinite sum. Then use an
appropriate formula to write it as a quotient of two integers.
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- Write out the addition and multiplication tables for 5.arrow_forwardProve by induction that 1+2n3n for n1.arrow_forward49. a. The binomial coefficients are defined in Exercise of Section. Use induction on to prove that if is a prime integer, then is a factor of for . (From Exercise of Section, it is known that is an integer.) b. Use induction on to prove that if is a prime integer, then is a factor of .arrow_forward
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