Artificial Intelligence cs607 5th ASsignment July, 2010

[Xpert]

Objective
o To learn and understand basic concepts of FUZZY logic.
Problems
Q 1) What properties do the classical logic operators posses that are not shared by
fuzzy logic operators? MARKS 2
Q 2) When combining the fuzzy numbers A and ⌐A, what fuzzy logical operators
should be used? MARKS 2
Q 3) When combining the fuzzy quantities A and A, what fuzzy logical operators
should be used? MARKS 2
Q 4) For example we have given the following prepositions: MARKS 3
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: MARKS 3
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 6) A complex logical proposition consists of elementary propositions connected
by 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)
MARKS 8 (4+4)