3 - The University of Sydney MATH 1004 Second Semester...

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The University of Sydney MATH 1004 Second Semester Discrete Mathematics 2011 Tutorial 3 Week 4 1. Defne f : N N by f ( x ) = x + 1. Determine whether or not f is (a) one-to-one; (b) onto. 2. Each oF the Following sets oF pairs may or may not represent a Function From { 1 , 2 , 3 } to { a, b, c, d } . { (1 , d ) , (2 , b ) , (3 , d ) } , { (1 , c ) , (2 , a ) , (3 , b ) } , { (1 , a ) , (3 , b ) } { (1 , a ) , (1 , c ) , (3 , d ) } , { (2 , b ) , (3 , c ) , (1 , d ) } ( i ) IdentiFy the sets which represent Functions and determine which oF these are one-to-one. ( ii ) Explain clearly why each oF the sets does or does not represent a Function. ( iii ) Explain clearly why each oF the sets does or does not represent a one-to- one Function. 3. ( i ) Let A = {- 1 , 2 , 3 , 5 , 7 , 11 } and let B = { 1 , 2 , . . ., 200 } . Is the Function f : A B given by f ( x ) = x 2 one-to-one? ( ii ) Now suppose that A = {- 2 , - 1 , 2 , 3 , 5 , 7 , 11 } and B = { 1 , 2 , . . ., 200 } . Is
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3 - The University of Sydney MATH 1004 Second Semester...

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