3.9. Given the continuous, noninteractive fuzzy sets A and B on universes X and Y, using Zadeh's notation for continuous fuzzy variables, A = {{ a for x € [0, +10]. 0.2|y| B = for y e [0, +5]. y as seen in Figure P3.9a: (a) Construct a fuzzy relation R for the Cartesian product of A and B. (b) Use max-min composition to find B', given the fuzzy singleton A' = (see Figure P3.9b). Hint: You can solve this problem graphically by segregating the Cartesian space into

Let A = {1, 2, 3},         B = {{1}, 2, {1, 3}},         C = {1, {1}, 3}.   Compute the following sets:                                                                         2A∩C − B,         (A ∩ B) × (A − C),         (B ∪ C) − A.

6. Use rules of inference to show that if Vr(P(x) v Q(x)) and Vr((-P(x) ^ Q(x)) → R(x)) are true, then Vx(-R(x) → P(x)) is also true, where the domains of all quantifiers are the same. 7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n e Z, n³ +n is even. (c) Prove that for all n e Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.

Reduce the following lambda calculus terms to the normal form. Show all intermediate steps, with one beta reduction at a time. In the reduction, if necessary, assume that you are supplied with extra rules that allow you to rehice the additLion of two natural mumbers into the corresponding result. (Az. 2) (Ny. y y) (\x. z a).

Being able to get in touch with others in various ways is a great asset, and the usage of social media makes this even easier?