# For the given f : A → B , decide whether f is onto and whether it is one-to-one. Prove that yourdecisions are correct. a. Α = Z × Z , B = Z × Z , f ( x , y ) = ( y , x ) b. Α = Z × Z , B = Z , f ( x , y ) = x + y c. Α = Z × Z , B = Z , f ( x , y ) = x d. Α = Z , B = Z × Z , f ( x ) = ( x , 1 ) e. Α = Z × Z , B = Z , f ( x , y ) = x 2 f. Α = Z × Z , B = Z , f ( x , y ) = x 2 + y 2 g. Α = Z + × Z + , B = Q , f ( x , y ) = x / y h. Α = R × R , B = R , f ( x , y ) = 2 x + y

### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230

### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
Publisher: Cengage Learning,
ISBN: 9781285463230

#### Solutions

Chapter
Section
Chapter 1.2, Problem 13E
Textbook Problem

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