# Math Help - boolean product of a matrices

1. ## boolean product of a matrices

How do I find the boolean product of matrices? I know I need to pair up numbers with ^ and place v in between, but I don't know which numbers to pair up.

For example:

A= 1 0 0 1 and B= 1 0
0 1 0 1 0 1
1 1 1 1 1 1
1 0

How do I know which numbers to pair up?

2. Nevermind! I think I hit a break through!

3. Hello,

Originally Posted by sjenkins
How do I find the boolean product of matrices? I know I need to pair up numbers with ^ and place v in between, but I don't know which numbers to pair up.

For example:

A= 1 0 0 1 and B= 1 0
0 1 0 1 0 1
1 1 1 1 1 1
1 0

How do I know which numbers to pair up?
By making the product of the matrices :

$A=\begin{pmatrix} 1&0&0&1 \\ 0&1&0&1 \\ 1&1&1&1 \end{pmatrix} \qquad B=\begin{pmatrix} 1&0 \\ 0&1 \\ 1&1 \\ 1&0 \end{pmatrix}$

Like the boolean language, if you have $0 \wedge 0$ or $1 \wedge 0$ or $0 \wedge1$, the result will be $0$.
If you have $1 \wedge 1$, the result will be $1$.

To make the product of two matrices, see here : Matrix multiplication - Wikipedia, the free encyclopedia
The difference between the boolean product and the common product is that $+$ will be replaced by $\vee$ and $*$ by $\wedge$.

The result is :

$A.B=\begin{pmatrix} (1 \wedge 1) \vee (0 \wedge 0) \vee (0 \wedge 1) \vee (1 \wedge 1) & (1 \wedge 0) \vee (0 \wedge 1) \vee (0 \wedge 1) \vee (1 \wedge 0) \\
(0 \wedge 1) \vee (1 \wedge 0) \vee (0 \wedge 1) \vee (1 \wedge 1) & (0 \wedge 0) \vee (1 \wedge 1) \vee (0 \wedge 1) \vee (1 \wedge 0) \\
(1 \wedge 1) \vee (1 \wedge 0) \vee (1 \wedge 1) \vee (1 \wedge 1) & (1 \wedge 0) \vee (1 \wedge 1) \vee (1 \wedge 1) \vee (1 \wedge 0) \end{pmatrix}$

4. You are so helpful, thank you for all the advice you have given to me in the past few days. I have been really struggling with this class.