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. $A'\cdot B = (A+B)'$

please someone who knows the answer please help me.

  • 1
    $\begingroup$ What problems are you having? $\endgroup$ – 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:

$$\begin {array}{c|c|c|c|c|c} \\ A&B&C&(A+B)&(A+B)+C&A+B+C \\ \hline T&T&T&T&T&T\\T&T&F&T&T&T\\F&F&T&F&T&T \end {array}$$

There are five more lines. Mine would usually be the first, second, and seventh lines in the table.

  • $\begingroup$ thanks for that. but our teacher had given us that way i mentioned earlier. i can add the things up but i cant get the last answer. i don't know how. how to show that its equal? $\endgroup$ – Charuka May 2 '13 at 17:06
  • $\begingroup$ @Charuka: what last answer do you mean? can you do the other five rows of the first table? $\endgroup$ – Ross Millikan May 2 '13 at 17:10
  • $\begingroup$ ok this is the question which is given to me as the assessment Using truth tables show that: A+B+C=(A+B)+C A⋅1=A A′⋅B=(A+B)′ the second one is hard i dont know how to make even the first step. but the first one i know how to do that A B C and (A+B) but we have to prove it right? the last answer should be (A+B)+C i dont know how to do that column. could you help me with those 3 questions. i am stuck $\endgroup$ – Charuka May 2 '13 at 17:13
  • $\begingroup$ @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. $\endgroup$ – Ross Millikan May 2 '13 at 17:19
  • $\begingroup$ @Charuka: you might look at Wikipedia. Their $\wedge$ is your $\cdot$ and their $\vee$ is your $+$ $\endgroup$ – Ross Millikan May 2 '13 at 17:20

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