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Union and Intersection of Intervals: ALEKS Answer

For A = {y | y > 1} and B = {y | y ≤ 6}, the union is all real numbers and the intersection is (1, 6].

Question

Union and intersection of intervalsA and B are sets of real numbers defined as follows:A = {y | y > 1}B = {y | y ≤ 6}Write A ∪ B and A ∩ B using interval notation. If a set is empty, write ∅.

Answers

A∪B=(−∞,∞)\boxed{A\cup B=(-\infty,\infty)} A∩B=(1,6]\boxed{A\cap B=(1,6]}

First translate each set:

A=(1,∞),B=(−∞,6].A=(1,\infty),\qquad B=(-\infty,6].

The union contains values in either set. Values at or below 6 are in BB, while values above 6 are in AA, so together the sets cover every real number.

The intersection contains only values in both sets. A number must be greater than 1 and less than or equal to 6, giving (1,6](1,6]. The parenthesis at 1 reflects the strict inequality y>1y>1; the bracket at 6 reflects y≤6y\le6.

Evidence boundary

This answer is limited to the exact sets A = {y | y > 1} and B = {y | y ≤ 6}. Endpoint inclusion follows the strict and non-strict inequalities in that version; no endpoints from other ALEKS variants are used.

Sources

These references support the concepts and methods used in the explanation above.

Union and Intersection of Intervals ALEKS Answer | Verla