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I’m constructing a truth table for statements “A”, “B”, “C”, and the composite statement “A AND B AND C”.

I’m pretty sure I constructed the table correctly, but I have a question about calculating all the possible combinations of “true” and “false” for three different variables:

Can you use exponents to solve this question?

In other words, 2^3=8, where the base is the possible number of values (for a logic statement, it can only be 2), and the exponent is the number of variables (in this case 3)? Which would mean there are eight combinations of “true” and “false” for three statements (variables)?

Can someone point me in the direction of where I can learn more about this? I would like to able to determine the possible combinations of “true” and “false” for any number of statements or variables.

The other aspect about the truth table I noticed is that the first and last row of truth values are “T” or “F”, the leftmost column is four “T’s”, then four “F’s”. The center column is two “T’s”, then two “F’s”; two “T’s”, then two “F’s”. The rightmost column goes back-and-forth between “T” and “F”. Does it have to be this way? Less important question, but I was curious to ask.

Any help would be appreciated. Thanks!

Question from book.

Truth table.

Peter G. Morales
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  • Your truth table is correct. The number of truth tables which can be constructed using $n$ (independent) statements is $2^n$ since there are two possible truth values for each of the $n$ statements. This is an application of the Multiplication Principle in combinatorics. As for recommending a source for learning combinatorics, it would help to know your mathematical background and why you need to learn combinatorics. – N. F. Taussig Mar 14 '22 at 09:55
  • I don’t have a high level background in math. I’m studying math, now, to work my way up to be able to study electrical engineering and computer science. – Peter G. Morales Mar 15 '22 at 07:03
  • Since you are interested in learning computer science, a good place to start learning the basics of combinatorics would be a discrete mathematics book. Kenneth H. Rosen's Discrete Mathematics and Its Applications has a nice section on combinatorics. On the whole, I think Rosen's book works better as a reference than as a text since it is so comprehensive. Discrete Mathematics by Gary Chartrand and Ping Zhang is well-written, but I think Rosen does a better job with enumeration problems in combinatorics. I am not familiar with the texts by Susanna Epp or Edward Scheinerman. – N. F. Taussig Mar 15 '22 at 09:40
  • Thank you for the recommendations! – Peter G. Morales Mar 15 '22 at 20:52

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