More on AND

This page contains more examples of the use of AND.

The logical operator AND is written && when writing a program in Java. (For example, $6-6=0$  && $1\leq 2$)

Often T is written for true and F for false.

Example 1

Find the truth value of $6-6=0$ AND $1\le 2$.

Answer: (This is the same as asking for the truth value of $6-6=0$ AND $1\le 2.$)

Firstly we need to determine the truth values of $6-6=0$ and of $1\le 2$:

  • $6-6=0$ is T (true)
  • $1\le 2$ is T

We have $\underbrace{6-6=0}_{T}$ AND $\underbrace{1\le 2}_{T}$. That is, we have T AND T.

The truth table for AND shows that T AND T is T. The answer is T.

Example 2

Find the truth value of $2+2=10$ AND $1\le 2$.

Answer: (This is the same as asking for the truth value of $2+2=10$ AND $1\le 2.$)

$2+2=10$ is F (false) and $1\le 2$ is T (true). So we have $\underbrace{2+2=10}_{F}$ AND $\underbrace{1\le 2}_{T}$ which is F AND T. From the truth table for AND we see that F AND T, which is the same as F AND T, is F. The answer is F.

Example 3

Find the truth value of $2+2=10$ AND $2\times 2=22$.

Answer: $2+2=10$ is F and $2\times 2=22$ is F. So we have $\underbrace{2+2=10}_{F}$ AND $\underbrace{2\times 2=22}_{F}$ which is F AND F. From the truth table for AND we see that F AND F is F. Therefore F AND F is F. The answer is F.

Example 4

Find the truth value of $1\le 2$ AND $2+2=10$.

Answer: We have $\underbrace{1\le 2}_{T}$ AND $\underbrace{2+2=10}_{F}$ which is T AND F. From the truth table for AND we see that T AND F is F. The answer is F.

Your Turn

Find the truth value of each statement (that is, decide whether each is true or false).

$5-3=0$ AND $-1\lt 1$
The sky is always red AND Finnish is the main language of Australia.
$23\le 100$ AND $0=0$
$23\le 100$ AND $0+1=0$