# More on 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.

 $5-3=0$&&$-1\lt 1$ 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 $23\le 100$&&$0+1=0$ True False