Given that S,T CR are nonempty, bounded subsets of the set of real numbers. State whether True or False. Justify your answer in each case. (a) Then sup (SnT) < sup S. (b) Let U = {s+t:s€ S,t e T}, then sup U = sup S + sup T (c) Suppose that S := {1+ " : n e N}, and T := and sup T = 2. {1 - ": n e N}, then inf S = 0 (-1)"

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A: The given function is f(x)=ln5x-x24

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A:

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A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

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A: Solution:

Q: A and B are sets of real numbers defined as follows. A-(: |2> 2} B-(: |258} Write AnBand AUB using…

A: Solution:   Given that A &amp; B are sets of real numbers such thatA = z | z&gt;2B = z | z≤8

Q: Pex)=\X+14 aud hex)= x-1 state functions. following domains, of the following 4sing interval…

A:

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A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

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A: This is the question from the topology.

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A: From the given function

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A: