
Problem 3.11. Prove the validity of the following argument.
1.
p→(q+r′)
2.
s→r
3. p
4.
q′
5.
∴s′
Solution 3.11. Validity of the argument is given below.
1. p→(q+r′) [1]
2. s→r [2]
3. p [3]
4. q′ [4]
5. q+r′ [1 and 3, Modus Ponens]
6. r→q [5, since r→q ≡ r′+q]
7. s→q [2 and 6, Chain Rule]
8. s′ [4 and 7, Modus Tollens]
Problem 3.12. Consider the fuzzy rule R : If service is good en customer is satis ed. Related uni-
verses are service-rating = {a, b, c, d, e}, and satisfaction-grade = {1, 2, 3, 4, 5} where the service-ratings a,
b, c, d, e a
r
e in des
cendin
g order and the satisfaction-grades 1, 2, 3, 4, 5 are in the ascending or ...