Hi,

I'm going to have a 'easy' maths exam (it's meant to be easy, it's not easy for me at all) in which we are expected to write out truth tables...

Can someone please mention the basic rules that I can apply...

Thank you!

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- Jun 7th 2010, 09:42 AMStudent122How can you make Truth Tables in a exam?
Hi,

I'm going to have a 'easy' maths exam (it's meant to be easy, it's not easy for me at all) in which we are expected to write out truth tables...

Can someone please mention the basic rules that I can apply...

**Thank you!** - Jun 7th 2010, 09:48 AMundefined
A truth table will list some number of arguments and specify the corresponding truth value when a logical operation is performed, for all possible inputs. So, here's a truth table for AND

Code:`p q p AND q`

= = =======

F F F

F T F

T F F

T T T

It is possible to take more than two arguments, for example

Code:`p q r (p AND q) OR r`

= = = ==============

F F F F

F F T T

F T F F

F T T T

T F F F

T F T T

T T F T

T T T T

F F F <--> 0 0 0

F F T <--> 0 0 1

F T F <--> 0 1 0

...

T T T <--> 1 1 1

where I'm using <--> to mean corresponds with. - Jun 7th 2010, 09:50 AMrowe
Your truth table will have $\displaystyle 2^n$ rows, where n is the number of variables you have. Start on the last variable, and write out T, F, T, F on each row $\displaystyle 2^n$ times.

So for instance, if you have three variables:

A B C

You, want to write alternating T, F for C, 2^3 = 8 times.

Then, you write alternating T, T, F, F for B,

Then, you write alternating T, T, T, T, F, F, F, F for A - Jun 7th 2010, 10:27 AMSoroban
Hello, Student122!

There is no easy way to explain Truth Tables.

Perhaps an example will help.

I'll deliberately break this up into separate steps.

They can be combined in one truth table, of course.

Example .Construct the truth table for: .$\displaystyle \bigg[(p \vee q) \:\wedge \sim p\bigg] \;\to\; q$

. . $\displaystyle \begin{array}{c|c||ccccccc}

p & q & \bigg[(p & \vee & q) & \wedge & \sim p\bigg] & \to & q \\ \hline

T & T & T && T && F && T \\

T & F & T && F && F && F \\

F & T & F && T && T && T \\

F & F & F && F && T && F

\end{array}$

. . . . . . . . . $\displaystyle \searrow\;\; \swarrow$

. . $\displaystyle \begin{array}{c|c||ccccccc}

p & q & \bigg[(p & \vee & q) & \wedge & \sim p\bigg] & \to & q \\ \hline

T & T & & T & & & F & & T \\

T & F & & T & & & F & & F \\

F & T & & T & & & T & & T \\

F & F & & F & & & T & & F

\end{array}$

. . . . . . . . . . . . $\displaystyle \searrow\qquad\swarrow$

. . $\displaystyle \begin{array}{c|c||ccccccc}

p & q & \bigg[(p & \vee & q) & \wedge & \sim p\bigg] & \to & q \\ \hline

T & T & & & & F & & & T \\

T & F & & & & F & & & F \\

F & T & & & & T & & & T \\

F & F & & & & F & & & F

\end{array}$

. . . . . . . . . . . . . . . . . . $\displaystyle \searrow\quad\;\; \swarrow$

. . $\displaystyle \begin{array}{c|c||ccccccc}

p & q & \bigg[(p & \vee & q) & \wedge & \sim p\bigg] & \to & q \\ \hline

T & T & & & & & & T& \\

T & F & & & & & & T & \\

F & T & & & & & & T & \\

F & F & & & & & & T &

\end{array}$

Hope this helps . . .