9.G. Prove the Cantor Intersection Theorem by selecting a point xn from Fn and then applying the Bolzano-Weierstrass Theorem 8.13 to the set {æn:n e N}.

2.1 Let sets A, B, and C be fuzzy sets defined on real numbers by the membership functions 1 pHa(x) =+10" 1 H(x) = 10* Hi(x) x+1 Determine mathematical membership functions and graphs of each of the followings : а) AU B, BоC, b) AUBUC, AOBOC c) Anī, BUC d) AOB, ĀU B 2.2 Show the two fuzzy sets satisfy the De Morgan's Law. 1 HA(x) = 1+(x-10) 1 HB(x) = 1+x 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded middle. a) H,(x) =- 1+x 60 / 340 b) 4 3D {(а, 0.4), (b, 0.5), (с, 0.9), (d, I)} 2.4 Determine complements, unions, and intersections of the following sets by using Yager's operators for o = 1, 2 a) A = {(a, 0.5), (b, 0.9), (c, 0.1), (d, 0.5)} 1 b) дл(х) —. 1+x 2.5 Compute the complements of the following sets by Yager's complements w = 1, 2. а) А — {(а, 0.5), (b, 0.9), (с, 0.3)} 1 b) H,(x) = 1+(x–1) 52 2. The Operation of Fuzzy Set 2.6 Compute the complements of the following sets by using Probabilistic, Bounded, Drastic, and Hamacher…

1. Find the supremum, infimum, maximum, and minimum of each subset of R, if it exists. a. A = sup A max A inf A U[-1-] TEN min A = {":neN} b. B = sup B max B inf B min B c. C = {re Q:r² ≥ 1} sup C max C inf C min C Q Search DOLL 1