With this dictionary representation of functions in place, write the following t

Question

With this dictionary representation of functions in place, write the following three Python functions:

is_injective: This function accepts a mathematical function (in dictionary form) and returns a Boolean value -- True if the mathematical function is injective and False otherwise. Examples:

Note that the examples illustrate that your is_injective must work on mathematical functions from any finite set to any other finite set; don't assume that we only use numbers.

is_surjective: This function accepts a mathematical function (in dictionary form) and a set, written as a list, that gives the codomain of the function and returns a Boolean value -- True if the mathematical function is surjective and False otherwise. Examples:

is_bijective: This function accepts a mathematical function (in dictionary form) and a set, written as a list, that gives the codomain of the function and returns a Boolean value -- True if the mathematical function is bijective and False otherwise. Examples:

Explanation / Answer

def is_injective(dict):
   vals = dict.values()
   # set does not contain duplicates. injective should not contain duplicates.
   if(len(vals) == len(set(vals))):
       return True
   return False
print "-----Injective----"
print is_injective({0: 8, 1: 8, 2: 9, 3: 9})
print is_injective({'a': 'x', 'b': 'y', 'c': 'z'})

# each domain value should be a value in dict, else return false
def is_surjective(dict,domain):
   for i in domain:
       if i not in dict.values():
           return False
   return True
print "-------Surjective---------"
print is_surjective({0: 8, 1: 8, 2: 9, 3: 9}, [7,8,9])
print is_surjective({0: 8, 1: 8, 2: 9, 3: 9}, [8,9])
print is_surjective({'a': 'x', 'b':'y', 'c':'z'}, ['x','y','z','t'])

# bijective only if injective and surjective.
def is_bijective(dict,domain):
   if(is_injective(dict) and is_surjective(dict,domain)):
       return True
   else:
       return False
      
print "--------------Bijective----------------"
print is_bijective({0: 8, 1: 8, 2: 9, 3: 9}, [7,8,9])
print is_bijective({0: 8, 1: 8, 2: 9, 3: 9}, [8,9])
print is_bijective({'a': 'x', 'b':'y', 'c':'z'}, ['x','y','z','t'])
print is_bijective({'a': 'x', 'b':'y', 'c':'z'}, ['x','y','z'])

# sample output

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.