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discrete mathematics, please do number 4 and 5 only see the attachments. 253-p2 equivalence prover assignment for further detail.


(4) It can be cumbersome to prove propositional equivalence. It is easier if we let a
computer do that. Write a script that contains the following:
(a) The function are_equivalent2 from class.
(b) The following propositional functions:
contrapositive_left (p, q) that returns p => q
. contrapositive_right (p, q) that returns -q - -p
. absorption1 (p,q) that returns p V (PA q)
. absorption2(p, q) that returns p / (p V q)
. left (p,q) that returns p.
(c) The function calls
. are_equivalent2 (contrapositive_left, contrapositive_right)
are_equivalent2 (absorption1, contrapositive_right)
are_equivalent2 (absorption1, left)
. are_equivalent2 (absorption2, left)
(5) Now do the same for propositional functions in three variables.
(a) Write a function are_equivalent3(F, G) that for two propositional functions F
and G in three propositional variables, that proves propositional equivalence of
F and G or gives a counterexample. If F and G are equivalent, the truth table
for the functions along with a conclusion should be printed. If F and G are not
a counterexample should he printed for

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