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Q6. (8 pts) Find explicit bijections to prove the following. 6.a. The set of even positive integers has the same cardinality as the set of odd positive integers. 6.b. The sets

`R`

and

`(0,1)`

have the same cardinality. [HINT: You may find the function arctan

`x`

useful.] 6.c. The sets

`{x:EEainZ_()>1x=(1)/(a)}`

and

`{x:EEainZ_()>=1x=(1)/(a)}`

have the same cardinality. 6.d. The sets

`(0,1)`

and

`(0,1]`

have the same cardinality. [HINT: You may find the bijection in part 6.C. useful.]