MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

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 BHence, 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 5Hence, 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 Bbecause if a bijection exist between two sets then there cardinalities are same but A and B have different cardinalitiesA has cardinality 4 and B has cardinality 6