Question

Let f : A --> B where (8 points) f = {(a, 1), (b, 3), (c, 5), (d, 2)) a. What is the co-domain of f 3. Let A= {a, b,c,d) and B= {1, 2, 3, 4, 5, 6). b. What is the range of f? c. Is f-1 a function Explain . d. Can there exist a bijection between A and B? Explain

Answer 1

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