Mark each true or false and justify.

1) If a nonempty subset of real numbers has an upper bound, then it has a least upper bound.

2) Every nonempty bounded subset of real numbers has a maximum and a minimum.

3) Ifmis an upper bound forSandm'<m, thenm'is not an upper bound forS.4) For each real number

xand eachE> 0, there exists annelement of the natural numbers such thatnE>x.