Problem 3. Let S : {:5 E Q : 3:2 lt; 2}. (a) Is 5' a countable or uncountable set? Explain. (b) State the Completeness Axiom. Does sup 5' exist in

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Can someone help me with the proof of this question a and b please

Problem 3. Let S : {:5 E Q : 3:2 < 2}.(a) Is 5' a countable or uncountable set? Explain.(b) State the Completeness Axiom. Does sup 5' exist in Q? In R? Explain. (c) Show that there is a sequence of rational numbers as” with x: —> 2. Hint: use the properties of thesupremum to construct a sequence {mm} in S with 3% —> sup 5' in R.