In: Computer Science
It is known that the sentence E: if (if P then not (Q or R) else not P) then (not (Q and S) if and only if (not Q or not S)). Investigate whether I = {S ← false, R ← false, Q '← true, P ← false} interpretations are interpretations for sentence E.
if (if P then not (Q or R) else not P) then (not (Q and S) if and only if (not Q or not S))
The sentence can be written as:
(P→((Q
R)
P))→((
Q
S)→
(Q
S))
Given, the statement
I = {S ← false, R ← false, Q '← true, P ← false}
P | Q | R | S | ![]() |
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P→(![]() ![]() ![]() ![]() |
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(P→(![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
T | T | T | T | F | F | F | F | T | T | T | T | T | T | T |
As the conclusion is true for the given interpretation.
Therefore, the interpretation I are interpretations for sentence E.