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 : O 6 O’, f(d) = 2d - 1, d 0 O. g : ø 6 O, g(n) = 2n + 1, n 0 ø. Using only the concept of function composition, can there be a bijective map from ø to O’? If so, compute it. If not, explain in details why not. ..................................................................................................................................... [2+8] b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W, X, Y and Z. We define the relation: A Sesotho word x is related to another Sesotho word y if x begins with the same letter as y. Determine whether or not this is an equi
) 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 : O 6 O’, f(d) = 2d - 1, d 0 O.
g : ø 6 O, g(n) = 2n + 1, n 0 ø.
Using only the concept of function composition, can there be a bijective map from ø
to O’? If so, compute it. If not, explain in details why not.
..................................................................................................................................... [2+8]
b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W,
X, Y and Z.
We define the relation: A Sesotho word x is related to another Sesotho word y if x
begins with the same letter as y.
Determine whether or not this is an equivalence relation.
If it is an equivalence relation then
1. Compute C(sekatana)
2. How many equivalence classes are there in all, and why?
3. What is the partition of the English words under this relation?
If it is NOT an equivalence relation then explain in details why it is not
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Write in C++ a polymorphic and recursive function, print(x, n, w),
which can print an object, x, the given number of times, n, separated by the user’s choice of white space character, w.
Both n and w must be “default arguments”. The default value of “n” must be 1 and the default value of “w” must be the space character.
(1) (2) (3)
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