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I am not currently in university, but I am going through a discrete mathematics text book from when I was in university. In the text book examples, there was a problem that I looked through and I thought it would be good to apply a truth table to it. I am unsure about my answer, so please let me know if I got something wrong. Here is the statement which I'm using to create the truth table.

'You cannot ride the roller coaster if you are under four feet tall unless your are older then 16 years old.'

If we break this down, we get the propositional variables q(You can ride the roller coaster), r(You are under four feet tall) and s(You are older than sixteen years old).

We can use these to create the propositional statement (r ^ ¬s) ⇒ ¬q

Here is the truth table I have formulated.

\begin{array}{|c|c|c|c|c|} \hline r & s & (r \land ¬s) & ¬q & (r \land ¬s) \rightarrow \neg q \\ \hline T & T & T & T & T \\ T & F & F & F & T \\ F & T & F & T & T \\ F & F & F & F & T \\ \hline \end{array}

After looking through this truth table, I noticed that there was a missing condition in the final conditional statement, specifically, if (r ^ ¬s) is T and ¬q is F. Therefore, I created a new truth table as seen below.

\begin{array}{|c|c|c|} \hline (r \land ¬s) & \neg q & (r \land ¬s) \rightarrow ¬q \\ \hline T & T & T \\ F & T & T \\ T & F & F \\ F & F & T \\ \hline \end{array}

Thoughts? The book did not ask for a truth table, but I thought I would write one out anyway. Are there any corrections that should be made?

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    I mean; the simplest way you could do it is to construct two functions: tall(x) and age(x). Where tall(x) returns a 1 for people over 4 feet, age(x) returns a 1 for people over 16 and they both return a zero otherwise. Then you could write r=tall(x)+age(x) – 2017-01-23
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    @TheRedCameron Please look at how you typeset these truth-tables ... – 2017-01-23

2 Answers 2

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With 3 variables, your truth table should have $2^3 = 8$ rows, which are all 8 possible truth-value combinations of q, r, and s.

So, fill this out:

\begin{array}{|c|c|c|c|c|c|} \hline r & s & q & (r \land ¬s) & ¬q & (r \land ¬s) \rightarrow \neg q \\ \hline T & T & T & & & \\ T & T & F & & & \\ T & F & T & & & \\ T & F & F & & & \\ F & T & T & & & \\ F & T & F & & & \\ F & F & T & & & \\ F & F & F & & & \\ \hline \end{array}

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    Actually q is the truth value of riding the roller coaster. So it is not a variable, it is the value of the statement. The truth table will only have 4 rows. – 2017-01-23
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    @user400188 Sorry, but no. $q$ is a statement with its own truth-value, so when you put $(r \land \neg s) \rightarrow \neg q$ on a truth-table, you will have to treat it just like $s$ and $r$ – 2017-01-23
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    Keep in mind that we are creating a truth table for the English sentence and not finding the truth table for the expression he crated. (For anyone new reading these; my first comment was on Bram28's un-edited answer which was was only that first sentence you see). – 2017-01-23
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"You cannot ride the roller coaster if you are under four feet tall unless your are older then 16 years old."

Breaking this down we see that if a person is under four feet, they can still get on if they are old enough. Also if they are not old enough but they are sufficiently tall they may also board the ride.

From this we may create the truth table

truth table

where q, r and s each symbolize: q: You can ride the roller coaster r: You are under four feet tall s: You are older than sixteen years old