Question

Are the following equivalent?
1)x belongs to R-(-1,3)
2)x belongs to (- infinity to -1) union of [3,infinity)
3)x <= to -1 or x >=3.
can someone provide me detail explanation

Answer 1

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1) x belongs to R-(-1,3) means all real numbers excluding the numbers in the open interval (-1,3) which means excluding all points between -1 and 3 but including the
end points -1 and 3. Thus we can also write the condition as -infinity <x<=-1 or x >=3. In interval notation it is (-infinity,-1] U [3,infiity) where the square brackets [ and ] indicate
that the points -1 and 3 are to be included.
2) x belongs to (-infinity,-1) U [3,infinity) is different from the first case in that the point -1 is excluded here whereas it is included in the first case.
3) x <= to -1 or x >=3. . This is exactly same as case 1 as explained above
So cases 1 and 3 arre equivalent while 2 is different