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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. here both AND and && are used because you need to know both.
Often T is written for true and F for false.
Example 1
Find the truth value of $6-6=0$&&$1\le 2$.
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 $\underbrace{6-6=0}_{T}$&&$\underbrace{1\le 2}_{T}$. That is, we have T&&T.
The truth table for && shows that T&&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 $2+2=10$&& $1\le 2.$)
$2+2=10$ 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 && we see that F&&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 && we see that F&&F is F. Therefore F AND F is F. The answer is F.
Example 4
Find the truth value of $1\le 2$&&$2+2=10$.
Answer: We have $\underbrace{1\le 2}_{T}$&&$\underbrace{2+2=10}_{F}$ which is T&&F. From the truth table for && we see that T&&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).
$5-3=0$&&$-1\lt 1$ | |
The sky is always red AND Finnish is the main language of Australia. | |
$23\le 100$ AND $0=0$ | |
$23\le 100$&&$0+1=0$ |
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