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Python question - Discrete structure and Formal Language

Good day,

(Please look at the attachment to have the real questions). This is logics Formal Language and needs to be done in Python.

Write programs in Python to solve the following problems. It is important to note that

you will learn more by testing your programs with di erent inputs, e.g., domains D and the predicates P(x), and Q(y; z).

1. [10 Points] We studied the universal (V) and existential (E) quanitiers. De ne the

domain D as a set of values and de ne the predicate p(X) as you wish. For instance,

you can de ne D = {1; 2;    ; 10}, and assume P(1) and P(2) are true and that P(3)

is false. Similary de ne the true predicates in Q. By defult, consider a predicate to be

false if it is not given to be true. In databases, this is referred to as the closed world

assumption. Write two functions in Python to return the correct value (true or false)

for the well-formed formluas Vx P(x) and Ex P(x). Run enough tests to make sure it

works properly and terminates on all the valid inputs.

2. [20 Points] Repeat problem 1 for the formula VxEy Q(x; y).

3. [15 Points] Use the truth table and develop a program in Python to classify the fol-

lowing well-formed formulas in propositional logic into tautology, contingency, or con-

tradiction.

(a). [-p & (p V q)] -> q

(b). r & ((p -> -r) & (-p -> -r))

(c). [p -> (q -> r)] -> [(p -> q) -> r]

4. [5 Points] Use the truth table approach and develop a program that decides whether

(p -> q) -> (r -> s) and (p -> r) -> (q -> s) are logically equivalent. If not, explain.

Compétences : Python

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