Which of the following functions f determine an isomorphism from A onto B? A = (z,*:0), B = (N, gcd, 1), where gcd is greatest common diviser f(x) = 1 for x=0 and f(x)=2 for all others x. A = (R,+;0), B = (R,*;1), f(x) = (x+1) (x-1). %3D A = (R,+;0), B = (RP,*;1), f(x) = 3^x, where RP is the set of positives real numbers. %3D A = (R/Q, +), B = (Q, +), f(x) = the smallest rational number bigger than x. %3D
Which of the following functions f determine an isomorphism from A onto B? A = (z,*:0), B = (N, gcd, 1), where gcd is greatest common diviser f(x) = 1 for x=0 and f(x)=2 for all others x. A = (R,+;0), B = (R,*;1), f(x) = (x+1) (x-1). %3D A = (R,+;0), B = (RP,*;1), f(x) = 3^x, where RP is the set of positives real numbers. %3D A = (R/Q, +), B = (Q, +), f(x) = the smallest rational number bigger than x. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Which of the following functions f determine an isomorphism from A onto B?
A = (Z,*:0), B = (N, gcd, 1), where gcd is greatest common diviser f(x) = 1 for x=0 and f(x)=2 for all others x.
A = (R,+;0), B = (R,*;1), f(x) = (x+1)(x-1).
A = (R,+;0), B = (RP,*;1), f(x) = 3^x, where RP is the set of positives real numbers.
A = (R/Q, +), B = (Q, +), f(x) = the smallest rational number bigger than x.
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