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