[Set Theory] If the universal set is the set of real numbers, is {[b,∞): b ∈ R} an algebra of sets?

[khloeeee101]

Can someone please help me answer this?

 

[lex]

Look up the definition:
e.g. click here
and check that each property applies, or show that one doesn't apply. E.g. does the set contain the empty set, is the complement in [MATH]\mathbb{R}[/MATH] of [MATH][1,\infty)[/MATH] a set of the form [MATH][b,\infty), b\in \mathbb{R}[/MATH] ? etc...

 

[pka]

Can someone please help me answer this?

Please tell us how your instructor/classnotes/textbook defines an algebra of sets.
As we see in this link there is no universal agreement on the definition.