Question 1158642
 Set-Builder Notation and Interval Notation.

Suppose A={ {{{x}}} is an element of real number: {{{-2 <=x < 5}}} } and B= ({{{-1}}}, {{{6}}}]

=>{{{A}}}={{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}},{{{3}}},{{{4}}}

=>{{{B}}}={{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}},{{{3}}},{{{4}}},{{{5}}},{{{6}}}


1. Find A U B and give the answer in interval notation. 

means: the new set that contains every element from either of {{{A}}} and {{{ B}}}

in your case {{{B}}} contains every element from {{{A}}} and some more, so union is actually  set {{{B}}}

{{{A}}} U {{{B}}}={{{B}}}={{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}},{{{3}}},{{{4}}},{{{5}}},{{{6}}}

in interval notation: ({{{-1}}}, {{{6}}}]


2. Write A (intersection) B as one set using set builder notation.

means: the new set that contains every element that is in both of the input sets; only things inside both of the input sets get added to the new set

in your case all elements of {{{A}}} are also elements of {{{B}}}, so intersection is actually  set {{{A}}}

{{{ A}}}∩{{{B}}}= {{{A}}}={{{-2}}},{{{-1}}},{{{0}}},{{{1}}},{{{2}}},{{{3}}},{{{4}}}


{ {{{x}}} is an element of real number: {{{-2 <=x < 5}}} }