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 $1\le 2$.
Answe r: (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 $1\le 2$.
Answe r: (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 $2\times 2=22$.
Answe r: $2+2=10$ 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 $2+2=10$.
Answe r: 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 $-1\lt 1$ | [ ]True [ ]False |
| The sky is always red AND Finnish is the main language of Australia. | [ ]True [ ]False |
| $23\le 100$ AND $0=0$ | [ ]True [ ]False |
| $23\le 100$ AND $0+1=0$ | [ ]True [ ]False |
Check Answer
That's correct! You should move on to this page to continue your explorations.
Not quite. Try these questions for more practice.
| Every computer program is written in FORTRAN AND Sydney is in NSW. | [ ]True [ ]False |
| $20+20=40$ AND $2\times 3=0$ | [ ]True [ ]False |
| $6\lt 10 AND $10\lt 20$ | [ ]True [ ]False |
| $10\lt 6$ AND $20\lt 10$ | [ ]True [ ]False |
Check Answer
That's correct! You should move on to this page to continue your explorations.
Not quite. Re-read this page and try these again