Answer with Step-by-step explanation:
Let A= {a, b,c,d} and B= {1, 2, 3, 4, 5, 6}
Define f:A→B
where f = {(a, 1), (b, 3), (c, 5), (d, 2)}
a. What is the co-domain of f
The co-domain or target set of a function is the set into which all of the output of the function is constrained to fall.
Here, all the values are constrained to fall on the set B
Hence, co-domain={1, 2, 3, 4, 5, 6}
b. What is the range of f?
The set of all output values of a function is called range.
Here, on putting the values of set A we get the output values as:1,2,3 and 5
Hence, Range={1,2,3,5}
c. Is f 1-1 function Explain.
A function for which every element of the range of the function corresponds to exactly one element of the domain.
Yes, f is 1-1
(Since, every element of range i.e. 1,2,3 and 5 corresponds to only one element of set A)
d. Can there exist a bijection between A and B? Explain.
No, there cannot exist bijection from A to B
because if a bijection exist between two sets then there cardinalities are same but A and B have different cardinalities
A has cardinality 4 and B has cardinality 6