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Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 21E: 21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in...
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True or False

a)The product of any two irrational numbers is irrational.

b)If f:S→T is not one-to-one, then S and T do not have the same cardinality.

c)Suppose f:A→B has the property that for every x∈A, f(x) is a unique elementof B. Then f is one-to-one.

d)Every bounded set of real numbers has infinitely many upper bounds.

e)If u∈A and u is an upper bound of A, then u = supA.

f)If A is an infinite set of irrational numbers, then A is uncountable.

g)Every set of negative real numbers has a supremum.

h)There exists a set of negative real numbers whose supremum is positive.

i)If f:A→B and g:B→C are functions such that g◦f: A→C i s onto, then f is also onto.

j)The set [0,1] has the same cardinality as R.

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