Homework 13 solutions
(a) Yes; if ( )(1 ) = ( )(2 ) then by definition (1 ) = (2 ). But since is an injection
this implies that (1 ) = (2 ) and now, since is injective, 1 = 2 .
(b) Yes; suppose , then there exists such that () = since is onto . But sin
Homework 14 Solutions:
It suffices to show that there exists a bijection from to . (Since we know that a linear function of
nonzero slope is an invertible function from to itself) it seems reasonable to consider : ,
defined by () = , as a candidate for