Chapter 1, Problem 1VR

Complete each statement with the correct term from the column on the right. Some of the choices may not be used and some may be used more than once.

addition principle

multiplication principle

union

set-builder

empty set

absolute value

disjunction

inequality

intersection

distance

interval

disjoint sets

compound

conjunction

A(n) _________is a sentence containing $\text{<,}\le ,>,\ge ,\text{ or }\ne$. [1.4a]

To determine

The blank provided in the statement “A (n) ________ is a sentence containing

$<,\le ,>,\ge ,\text{or}\ne$”

Answer to Problem 1VR

Solution:

An inequality is a sentence containing $<,\le ,>,\ge ,\text{or}\ne$ So, option (h) is correct.

Explanation of Solution

Given Information:

The provided options are:

(a) addition principle

(b) multiplication principle

(c) union

(d) set-builder

(e) empty set

(f) absolute value

(g) disjunction

(h) inequality

(i) intersection

(j) distance

(k) interval

(l) disjoint sets

(m) compound

(n) conjunction

An inequality is a relation that holds between two values when they are different.

It is a mathematical sentence formed by relating two expressions to each other using the symbols $<,\le ,>,\ge ,\text{or}\ne$.

Each of the symbols $<,\le ,>,\ge ,\text{or}\ne$ have some specific meaning which is given below:

$\begin{array}{cc}\text{Symbol}& \text{Meaning}\\ <& \text{less}\text{than}\\ \le & \text{less}\text{than}\text{or equal to}\\ >& \text{greater}\text{than}\\ \ge & \text{greater}\text{than}\text{or equal to}\\ \ne & \text{not}\text{equal}\text{to}\end{array}$

Thus, the complete statement is “An inequality is a sentence containing $<,\le ,>,\ge ,\text{or}\ne$ ”. So, option (h) is correct.