Question

Describe each set by listing:

(a) The integers strictly between -3 and 9.

(b) The negative integers greater than -10.

(c) The positive integers whose square roots are less than or equal to 4.

NOTE: Z is the set of integers, Q is the set of rational numbers, and Z the set of real numbers.

Short answer

(a) The list of the integers is $\left\{-2,-1,0,1,2,3,4,5,6,7,8\right\}$.

(b) The list of integers which in greater than -10 is $\left\{-9,-8,-7,-6,-5,-4,-3,-2,-1\right\}$.

(c) The positive integers whose square roots are less than or equal 4 are $\left\{1,2\right\}$.

Step-by-step solution

Write down the given data from the question.

The integer lies between -3 and 9.

The negative integer greater than -10.

Negative integer whose square is less than or equal to 4.

Determine the list of the integer which lies between -3 and 9.

(a)

The integer is lies between -3 to 9 that means the integer -3 and 9 do not included in the list.

Therefore, the list of the integer which strictly lies between -3 and 9 is $\left\{-2,-1,0,1,2,3,4,5,6,7,8\right\}$.

Hence the list of the integer is $\left\{-2,-1,0,1,2,3,4,5,6,7,8\right\}$.

Determine the list of the integer which is greater than -10.

(b)

The negative integer is greater than -10 therefore, -10 is not included into the list. Therefore, the list of integers of negative integer which is greater than -10 is $\left\{-9,-8,-7,-6,-5,-4,-3,-2,-1\right\}$.

Determine the list of the positive integers whose square roots are less than or equal to 4.

(c)

The positive integer which is less than 4 are 1,2 and 3. But the square root value or integers 1,2 and 3, are 1,4 and 9 respectively. But the square root of the integer 3 is greater than 4.

Hence the positive integers whose square roots are less than or equal 4 are $\left\{1,2\right\}$.