Chapter R2, Problem 1PE

To determine

The correct word or phrase to fill in the blank.

Answer to Problem 1PE

Solution:

The word/phrases which can be filled in the blanks of each statement can be given as:

1. Set.
2. Inequalities.
3. a is less than b.
4. c is greater than d.
5. 5 is not equal to 6.
6. Infinity, Negative infinity
7. $\left\{x|x>5\right\}$, Interval.
8. Excludes, includes.
9. Parenthesis.

Explanation of Solution

  $\left(a\right)$ In mathematics, a well-defined collection of elements is called a Set.$\left(b\right)$ The statements $a<b,a>b,\text{and }a\ne b$ are examples of Inequalities.

  $\left(c\right)$ The statement $a<b$ is read as “ais less thanb”.

  $\left(d\right)$ The statement $c\ge d$ is read as “cis greater than or equal tod”.

  $\left(e\right)$ The statement $5\ne 6$ is read as “5 is not equal to 6”.

  $\left(f\right)$ The symbol $\infty$ represents Infinityand $-\infty$ represents Negative infinity.$\left(g\right)$ The set of real numbers greater than 5 can be written in set-builder notation as $\underset{\_}{\left\{x|x>5\right\}}$ and in Intervalnotation as $\left(5,\infty \right)$ .

  $\left(h\right)$ We know that parentheses) or (indicate that an endpoint is excluded from the set. And the square bracket ] or [ indicates that an endpoint is included in the set.

Thus, the interval $\left(-2,\text{}5\right]$excludesthe value $-2$ and includesthe value 5.

  $\left(i\right)$ When expression interval notation, use a parenthesiswith infinity.