Question

Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate.

a) The set {S∈ R: x²-3x+2=0} is an infinite set.

b) The greatest interger function is continuous on R.

c) equation

d) Every integrable function is monotonic.

e) equation defines a binary operation on Q, the set of rational numbers.

06 Feb 2025
Answer :
Word Count : 162
a) False. Solve $x^2-3x+2=0\Rightarrow (x-1)(x-2)=0$, so the solution set is $\{1,2\}$, which is finite (two elements), not infinite. b) False. The greatest integer (floor) function $\lfloor x\rfloor$ _____ _______ _________ _______ _________.
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