Assignment #2 Solution

Show that drastic product and drastic sum (defined below) satisfy the law of contradiction
(𝐴 ∩ 𝐴̅ = ∅) and the law of excluded middle (𝐴 ∪ 𝐴̅ = 𝑋). [Hint: substitute the t-norm and s-norm
operation for intersection and union in the two laws, respectively]

Drastic product    x t y = x  if  y = 1    Drastic sum    x s y = y  if  x = 0

y  if  x = 1    x  if  y = 0
0 otherwise    1 otherwise




2.    [4 marks] Assume a fuzzy set




    A = [1.0,0.8,0.5,0.1,0]




defined on universe



X= 1,2




,3,4



,5 . Find all of

it’s unique    -cuts. Show how A can be expressed in terms of the family of all of its    -cuts.