a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define the bijections, f and g as:

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a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define
the bijections,f and g as:
f:0 0', f(d) = 2d 1, Vd e O.
g: N-0, g(n) = 2n + 1, Vn e N.
Using only the concept of function composition, can there be a bijective map from N
to O'? If so, compute it. If not, explain in details why not.
Transcribed Image Text:a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define the bijections,f and g as: f:0 0', f(d) = 2d 1, Vd e O. g: N-0, g(n) = 2n + 1, Vn e N. Using only the concept of function composition, can there be a bijective map from N to O'? If so, compute it. If not, explain in details why not.
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