Truth Tables

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May 4th 2011, 05:57 AM
Gall1987

Truth Tables

Hi,

I'm currently going through past exams papers as part of my revision for my upcoming exams, however the past papers that I am using do not include answers, so I'm not sure if I'm on the right track or not.

The question I'm working on is:

Which of the following columns (A) to (D) correctly completes the truth table for the expression?

The expression is 'p implies not q and r'. (I'm not sure how to type it mathematically).

p q r (A) (B) (C) (D)
F F F T T F T
F F T F T T T
F T F T T F T
F T T F T T T
T F F F F F F
T F T F T T F
T T F T F F T
T T T F F T F

I have tried to work it out and I've come out with column C. Can anybody tell me if that's correct, or where I might of gone wrong if it's not?
May 4th 2011, 06:01 AM
Ackbeet

A couple of comments.

1. What is your expression?
2. You can use WolframAlpha to generate truth tables thus.
May 4th 2011, 06:15 AM
Soroban

Hello, Gall1987!

Quote:

Which of the following columns (A) to (D)
correctly completes the truth table for the expression?

$\begin{array}{ccc|cccc} p & q & r & (A) & (B) & (C) & (D) \\ \hline \\[-4mm] F & F & F & T & T & F & T \\ F & F & T & F & T & T & T \\ F & T & F & T & T & F & T \\ F & T & T & F & T & T & T \\ T & F & F & F & F & F & F \\ T & F & T & F & T & T & F \\ T & T & F & T & F & F & T \\ T & T & T & F & F & T & F \end{array}$

What is "the expression"?
May 4th 2011, 06:19 AM
Gall1987

Quote:

Originally Posted by Ackbeet

A couple of comments.

1. What is your expression?
2. You can use WolframAlpha to generate truth tables thus.

Oh excellent, that looks like a good website to use. I have tried to use it to calculate the above equation though and it is displaying as this.

I can't get the equation to display correctly to calculate the truth table.
May 4th 2011, 06:21 AM
Gall1987

Quote:

Originally Posted by Soroban

Hello, Gall1987!

What is "the expression"?

The expression is P implies not q and r. Sorry, I thought I'd included it, but I'm not sure how to type it mathematically on here.
May 4th 2011, 06:34 AM
Ackbeet

Quote:

Originally Posted by Gall1987

Oh excellent, that looks like a good website to use. I have tried to use it to calculate the above equation though and it is displaying as this.

I can't get the equation to display correctly to calculate the truth table.

Yeah, that's weird. I tried a number of things that didn't work. I'm going to try the equivalent expression:

$p \to r$ if and only if

$\neg p \lor r.$

The result is here.

Update: Curiouser and curiouser! It worked this time, although there are no reassuring parentheses. The truth table is the correct one for your expression.