① / التاريخ Show that for any collection of topalgies onx the exist a unique Smallest to Plogy larger that each member of the collection. letxe anon empty set and F be 9 family of subsets of x such that FIXE F Fz: F1, F2 EF then FIUF₂ EF F3: FA EF Sorany Jε Athen A{FEAZGF Show that exists a unique to Pology - for x such that I-closed of subsets of X are Precisely the member of F.

Which of the following sets are closed under multiplication? 11. (i) X = {1, 2, 3, 4, ..., 30} (ii) Y = {all whole numbers except 8} (iii) Z= {all whole numbers except 17} C) (i) and (iii) A) (ii) only B) (iii) only D) (ii) and (iii)

Give an example of sets {An}n≥1 such that for each n ≥ 1, the set An ⊂ [0, 1] is both compact and connected, but the union of An n ≥ 1 is neither compact nor connected.

U=(4,5,6,7,8,9,10,11,12,13,14,15} U is the Universal set. A={x]x is a natural number and 9sx<14} B=(4,7,11,13,15} C=(4,5,6,13,14,15} Find the following: 1. A' (9,10,11,12,13,14,15) 2. Вс 3. AUC 4. (A B)

Let's define 5 sets as follows: A = {x,y,z} B = {p,q}_ C = {(x,p)} D = {x, p} E = {z} %3D List the members of the following sets: (а) Ах ВхЕ (b) (Ах В) — С (c) »(»(E)) |(d) \p(AUB) – D| Recall that p(A) is the power set of A and |A| denotes the number of elements |(cardinality) of A.

1/abs2mt.pdf?AWSAccessKeyld=ALMS%3aalms-storage%40advancity.com.tr&Expires=1619446530&Signature=kg 1 / 1 100% rite your name and student number on exam papers, Questions 1) We know that -5,-4,-3,-2,-1 and IN are well-ordered sets with respect to the trivial ordering. Let X= -3,-2,-1) UN. Prove that the poset X is a well- set with respect to the trivial ordering. ordered

I have the following question, please if able explain them in detail, I understand the general idea of indexed collections, but this one's just a bit too complex for me,