Chapter 1.6, Problem 62HP

To determine

To summarize: the difference between and compound inequalities and or compound inequalities.

Answer to Problem 62HP

Third one is False.

Explanation of Solution

Given information:

Calculation:

Let’s take and.

The operator and works only if both sides are true states, for example inequality with solutions,

  $x>2\text{and}x<1$

Can’t be true as see, because it is impossible for number to be both greater than 2 and lesser than 1, so one part of inequality solution is not true, therefore and operator is not working.

Let’s take or.

The operator or works if one of given two is true. It will take same example only merged with or.

  $x>2\text{or}x<1$

Now, see that there are numbers which are either greater than 2 or lesser than 1, therefore or operator is working.