Question

Write a program in Python to practice evaluating some logical expressions and determine whether the expressions are equivalent.

1. Read in a 0 or 1 integer value for each of the following variables: A, B, C, and D.

2. Use an if…else statement to change the 0 and 1 integer values into True and False Boolean values. Booleans in Python have to have this capitalization (True/False, not true/false or TRUE/FALSE) and shouldn’t contain double quotes (which makes them a String instead of a Boolean).

3. Use the converted True/False values to compute:

(( A ⋁ ¬C) ⋀ D)

in your code.

4. Use the values to compute:

(( ¬A) ⊕ B)

in your code.   HINT: There no Boolean ⊕ in Python. How would you write the code for the ⊕ operator using if statements and the 3 standard Boolean operators: AND, OR, and NOT?

5. Check to make sure that your program successfully calculates the result of both expressions.

6. If the truth values for the entered combination of A, B, C, and D values is the same for both expressions, (( A ⋁ ¬C) ⋀ D ) and (( ¬A) ⊕ B), print a message saying: “matches”

Otherwise print a message saying “untrue.” At this stage, your program will produce just one line of output per run.

7. We know that the operator ⟺ produces an answer of true ONLY when the two expressions produce the same result for EVERY combination of input values.

Change your program so instead of asking the user to enter an A, B, C, and D value, the computer uses loops to iterate through all the possible combinations of A, B, C, and D values. HINT: What possible values can A take on? What possible values can B take on? Nested loops will be your friend here.

For each set of A, B, C, and D values, print these input values on one line along with the computed match/untrue message for that line.   

Example: (( A ⋁ ¬C) ⋀ D)

Input                                 express 1           express 2           result

0      0      0      0              0                      1                      untrue

0      0      0      1              1                      1                      matches

…..

8. After all of the possible combinations of input have been considered, print a message saying “equivalent” if you find that the two expressions are equivalent. Print a message saying “not equivalent” if you find that the two expressions are not equivalent.

Answer 1

Here is the Python code:

A = int (input ("Input A, either 0 or 1:"))
B = int (input ("Input B, either 0 or 1:"))
C = int (input ("Input C, either 0 or 1:"))
D = int (input ("Input D, either 0 or 1:"))

A = False if A == 0 else True
B = False if B == 0 else True
C = False if C == 0 else True
D = False if D == 0 else True

def firstexpr (A, C, D):
    return ((A or (not C)) and D)
    
Expr1 = firstexpr (A, C, D)

def xor (firstbool, secondbool):
    return (firstbool != secondbool)

Expr2 = xor (not A, B)

if (Expr1 == Expr2):
    print ("Matches")
else:
    print ("Untrue")

Equivalent = True

for a in False, True:
    for b in False, True:
        for c in False, True:
            for d in False, True:
                lhs = int (firstexpr (a, c, d))
                rhs = int (xor (a, b))
                if lhs != rhs:
                    Equivalent = False
                comparison = "Matches" if lhs == rhs else "Untrue"
                print (int (a), int (b), int (c), int (d), "\t", lhs, rhs, comparison )
                
if Equivalent:
    print ("Equivalent")
else:
    print ("Not equivalent")