Problems
Q 1) What properties do the classical logic operators posses that are not shared byfuzzy logic operators?
Q 2) When combining the fuzzy numbers A and ¬A, what fuzzy logical operatorsshould be used?
Q 3) When combining the fuzzy quantities A and A, what fuzzy logical operatorsshould be used?
Q 4) For example we have given the following prepositions:
P = A ^ B
Q = A ν B
For all crisp truth values of A and B, construct a truth table for P, Q, P ^ Q, and
P ν Q.
Q 5) For example we have given the following prepositions: P = A -> BQ = A ν BFor all crisp truth values of A and B, construct a truth table for P, Q, P ^ Q, andP ν Q.
Q 6) A complex logical proposition consists of elementary propositions connectedby some logical operators.
For example, ¬ (P -> ¬ (Q -> R)
This complex logical proposition [¬ (P -> ¬ (Q -> R)] is called tautology, if
truth table has all true (1) values for this proposition. In opposite case, this
complex logical proposition [¬ (P -> ¬ (Q -> R)] is called contradiction, if
truth table has all false (0) values for this proposition.
Determine whether the following complex propositions are tautologies,
contradictions, or neither.
• (P ^ (P -> Q )) -> Q
• ((P -> Q ) ^ (Q -> R)) -> (P -> R)