Python Truth Tables 4 Functions need to be completed

# NOTE: # You must use small single letters for your variable names, for eg. a, b, c # You may use parenthesis to group your expressions such as 'a and (b or c)'

# Implement the following four functions: # truth_table, count_satisfying, is_tautology and are_equivalent

######## Do not modify the following block of code ######## # ********************** BEGIN *******************************

from functools import partial import re

class Infix(object): def __init__(self, func): self.func = func def __or__(self, other): return self.func(other) def __ror__(self, other): return Infix(partial(self.func, other)) def __call__(self, v1, v2): return self.func(v1, v2)

@Infix def implies(p, q) : return not p or q

@Infix def iff(p, q) : return (p |implies| q) and (q |implies| p)

# You must use this function to extract variables # This function takes an expression as input and returns a sorted list of variables # Do NOT modify this function def extract_variables(expression): sorted_variable_set = sorted(set(re.findall(r'\b[a-z]\b', expression))) return sorted_variable_set

# *********************** END ***************************

############## IMPLEMENT THE FOLLOWING FUNCTIONS ############## ############## Do not modify function definitions ##############

# This function calculates a truth table for a given expression # input: expression # output: truth table as a list of lists # You must use extract_variables function to generate the list of variables from expression # return a list of lists for this function def truth_table(expression): pass

# count the number of satisfying values # input: expression # output: number of satisfying values in the expression def count_satisfying(expression): pass

# if the expression is a tautology return True, # False otherwise # input: expression # output: bool def is_tautology(expression): pass

# if expr1 is equivalent to expr2 return True, # False otherwise # input: expression 1 and expression 2 # output: bool def are_equivalent(expr1, expr2): pass

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Test Code

# NOTE: # This is a Sample Test file. # This file is only for your reference. # Do not submit this file.

import PA1

# This is the function we will use to check the format of your truth table # Do not modify this function. def check_format(table, num_vars):

# check whether the table is a list assert type(table) is list, "table is not a list: %r" % table

# check whether every row in the table is a list for row in table: assert type(row) is list, "table is not a list of lists: %r" % table

# check if the table covers all possible combinations if len(table) < (2**num_vars): print('Truth table %r does not cover all combinations of variables. There should be %r combinations.' % (table, (2**num_vars))) return False

# check whether table has extra rows if len(table) > (2**num_vars): print('Truth table %r has extra rows. There should be %r combinations.' % (table, (2**num_vars))) return False

for row in table: # check if the table has missing columns if len(row) < (num_vars+1): print('One or more columns in the table are absent, total number of columns should be: %r' % len(row)) return False # check if the table has extra columns elif len(row) > (num_vars+1): print('Truth table has extra columns, total number of columns should be: %r' % len(row)) return False

return True

# sample test cases for each function # You should use different expressions to thoroughly test your output def main(): # sample test for truth_table function expression = 'a and b' tt = PA1.truth_table(expression) variables = PA1.extract_variables(expression)

# check format of the truth table if check_format(tt, len(variables)): print(' Truth table for the expression: ' + expression) print(tt)

# sample test for count_satisfying function count = PA1.count_satisfying(expression) # check format of return value assert type(count) is int, "count_satisfying: return value is not an int" % count print(' Number of satisfying values in the expression \'' + expression + '\' is: ' + str(count))

# sample test for is_tautology function is_a_tautology = PA1.is_tautology(expression) # check format of return value assert type(is_a_tautology) is bool, "is_tautology: return value is not a bool" % is_a_tautology if is_a_tautology: print(' The expression \'' + expression + '\' is a tautology!') else: print(' The expression \'' + expression + '\' is NOT a tautology!')

# sample test for are_equivalent function expr1 = 'not a or b' expr2 = 'a |implies| b'

tt1 = PA1.truth_table(expr1) variables1 = PA1.extract_variables(expr1)

if check_format(tt1, len(variables1)): print(' Truth table for expression 1: ' + expr1) print(tt1)

tt2 = PA1.truth_table(expr2) variables2 = PA1.extract_variables(expr2)

if check_format(tt2, len(variables2)): print(' Truth table for expression 2: ' + expr2) print(tt2)

are_equivalent_expressions = PA1.are_equivalent(expr1, expr2) assert type(are_equivalent_expressions) is bool, "are_equivalent: return value is not a bool" % are_equivalent_expressions if are_equivalent_expressions: print(' The expressions \'' + expr1 + '\' & \'' + expr2 + '\' are equivalent!') else: print(' The expressions \'' + expr1 + '\' & \'' + expr2 + '\' are NOT equivalent!')

if __name__ == '__main__': main()