Consider the Hasse diagram of the the following poset:   a) What are the maximal element(s)? b) What are the minimal element(s)? c) What are the upper bounds of { f, h, i }? d) What are the upper bounds of { d, e, g }? e) What are the lower bounds of { f, g, h }? f) What are the lower bounds of { d, e, g }? g) What is the least upper bound of { d, e, g }, if it exists? h) What is the greatest lower bound of { j, k, l }, if it exists? i) Is this poset a lattice? Why or why not?

Q: Prove that a subset of a set of measure zero has measure zero.

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Q: Set A is bounded above if and only if set -A is bounded below.

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Q: show that the Cantor set is a closed subset of R and has measure zero.

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Q: 6. Show that the span of this set is all of R?. {}}

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Q: Prove that intersection of any class of convex subsets of N is convex?

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A: Prove that the complement of a dense open subset of R is nowhere dense in R

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Q: 5. Show that if A and B are bounded subsets of R, then A U B is a bounded set. Show that sup(A U B)…

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Q: Give 3 different examples of norms on Z (set of integers)

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Q: Consider the subset W = {x € Q : xª > 1} of Q. 2.1 Express W using interval notation. 2.2 Is W…

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Q: Let A be a nonempty subset of R that is bounded below. Define the set B = {b: b is a lower bound of…

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Q: compact, then E must be infinite. Exercise 6.46. Prove that if E is a closed subset of a compact set…

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Q: show that empty set, X is an element of S intersection T in topology

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Q: Find an example of on a set X (G has or H of G which has le

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Q: (b) Prove that the complement of a dense open subset of RR is nowhere dense in R.R..

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Q: (b) Prove that the complement of a dense open subset of R is nowhere dense in R..

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Q: )Š is the smallest closed set in M such that S CS.

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Q: Consider the subset G {r• /2: x € Z} of R. Show that G is closed un- der addition.

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