**Unformatted text preview: **12 ) 4 )` Defire_ F : 2 _ D Z by the rule_ FLA ) = 2 - 3 ~ , for all\
integers ~`
i) is F one to one ? Prove or give a counter example_
ii) isf onto ? Prove of give a counter example_
b ) Define G : R _ R. by the relle G( X ) : 2 - 3 x for all real
numbers x. Is G onto? Pace or give a counter excomple
a ) ;) of is one to one : Suppose f (` ) = FLAz ) for some integers
My and rec By definition of F : 2 - 30, = 2- 3 ~`
\= - 3 21 = = 3 ~`
= ME = N Z
So f is one to one_
ii ) f is not onto : Consider 3 E Z we claim that } { FLA)?
for any integer ~ , because if there were an integer ~ such that
3 = f(m ), Then by chefinition off, 3= 2 - 3~`
= 1 = - 3 ~
- - 3 : ~
- I is not an integer , Hence 3 7 flow) for any integer ~`
and so F is not on to
6 ) G is onto : Suppose y ER. since YER, `y = 2 - 3 x
= 4 - 2 - 3 X
X - = 7- 2 =
2-7 = x
Itlace there exists an integer Such They g(x ) = Y . As was to be shown...

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- Fall '19
- NoProfessor
- Philosophy of language, Rational number, Define G