# Which of the following describes the union of the set of integers less than root20 and the set of integers greater than root 40?(a) no integers (b) two integers (c) three integers (d) all but two...

Which of the following describes the union of the set of integers less than root20 and the set of integers greater than root 40?(a) no integers (b) two integers (c) three integers (d) all but two integers (e) all integers
samhouston | Certified Educator

The square root of 20 is approximately 4.5

Set A:  {integers less than 4.5}

Set A:  {4, 3, 2, 1, 0, -1, -2, ...}

The square root of 40 is approximately 6.3

Set B:  {integers greater than 6.3}

Set B:  {7, 8, 9, 10, 11, 12, 13, ...}

A `uu` B = {..., -2, -1, 0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, ...}

In other words, the solution is all integers except of 5 and 6.

The answer is (D) all but two integers.

jackmacc2000 | Student

The answer is d) all but two integers. First of all, the union of two sets is the total of all the numbers in both of the sets. The integers less than root 20 is the integers less than 4, since 4 < root 20 < 5. The integers greater than root 40 is the integers greater than 7, since 7 > root 40 > 6. Thus, the union of both sets is all the integers, minus five and six, since those are the ones that are left out. Drawing a number line helps.