# truth table for followings

Hi I am new to this site.

I got an assessment to complete tomorrow. Its about Computer programming, and i am having trouble with these questions. Can anyone please help me.

Using truth tables show that:

1. $A+B+C = (A+B)+C$
2. $A\cdot 1 = A$
3. $A'\cdot B = (A+B)'$

• What problems are you having? – copper.hat May 2 '13 at 16:55

To make a truth table, you make columns for all the variables and rows for all combinations of truth values of the variables. Then you make as many columns as you want to assess the truth value of the statement in question. If you want to prove equality of two expressions, they must agree on all values of the truth value of the variables. It looks like you may have miscopied two of the problems: I would expect the first to be $A+(B+C)=(A+B)+C$ (because $+$ is usually defined as a binary operator) and the third is not correct. I'll give some lines of the first:
$$\begin {array}{c|c|c|c|c|c} \\ A&B&C&(A+B)&(A+B)+C&A+B+C \\ \hline T&T&T&T&T&T\\T&T&F&T&T&T\\F&F&T&F&T&T \end {array}$$
• @Charuka: To get $(A+B)+C$ you add the truth value you have in the $(A+B)$ column to the one in the $C$ column. The second one just has two lines because there is only one variable. $1$ is always True. As I said before, the third is not correct, so your verification should fail. – Ross Millikan May 2 '13 at 17:19
• @Charuka: you might look at Wikipedia. Their $\wedge$ is your $\cdot$ and their $\vee$ is your $+$ – Ross Millikan May 2 '13 at 17:20