More on OR
This page contains more examples of the use of OR.
The logical operator OR is written $||$ when writing a program in Java. (For example, $6-6=0 || 1\le 2$)
Often T is written for true and F for false.
Example 1
find the truth value of $6-6=0$ OR $1\le 2$.
Answer:
Firstly we need to determine the truth value of $6-6=0$ and of $1\le 2$: $6-6=0$ is T (true) and $1\le 2$ is T. We have $\underbrace{6-6=0}_{T}$ OR $\underbrace{1\le 2}_{T}$. That is, we have T OR T.
The truth table for OR shows that T OR T is T. The answer is T.
Example 2
Find the truth value of $2+2=10$ OR $1\le 2$.
Answer:
$2+2=10$ is F, (false) and $1\le 2$ is T (true). So we have $\underbrace{2+2=10}_{F}$ OR $\underbrace{1\le 2}_{T}$, which is F OR T. From the truth table for OR we see that F OR T is T. The answer is T.
Example 3
Find the truth value of $2+2=10$ OR $2\times 2=22$.
Answer: $2+2=10$ is F and $2\times 2=22$ is F. So we have $\underbrace{2+2=10}_{F}$ OR $\underbrace{2\times 2=22}_{F}$, which is F OR F. From the truth table for OR we see that F OR F is F. Therefore F OR F is F. The answer is F.
Example 4
Find the truth value of $1\le 2$ OR $2+2=10$.
Answer: We have $\underbrace{1\le 2}_{T}$ OR $\underbrace{2+ 2=10}_{F}$, which is T OR F. From the truth table for OR we see that T OR F is T. The answer is T.
Your Turn
Find the truth value of each statement (that is, decide whether each is true or false).
| $5-3=0$ OR $-1\lt 1$ | [ ]True [ ]False |
| The sky is always red OR Finnish is the main language of Australia. | [ ]True [ ]False |
| $23\le 100$ OR $0=0$ | [ ]True [ ]False |
| $23\le 100$ OR $0+1=0$ | [ ]True [ ]False |
Check Answer
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Not quite. Try these questions for more practice.
| Every computer program is written in FORTRAN OR Sydney is in NSW. | [ ]True [ ]False |
| $20+20=40$ OR $2\times 3=0$ | [ ]True [ ]False |
| $6\lt 10$ OR $10\lt 20$ | [ ]True [ ]False |
| $10\lt 6$ OR $20\lt 10$ | [ ]True [ ]False |
Check Answer
That's correct! You should move on to this page to continue your explorations.
Not quite. Try these again and re-read the above information.