1. ## 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?

2. You can use WolframAlpha to generate truth tables thus.

3. Hello, Gall1987!

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

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

What is "the expression"?

4. Originally Posted by Ackbeet

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.

5. 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.

6. 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:

$\displaystyle p \to r$ if and only if

$\displaystyle \neg p \lor r.$

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.