# Thread: Compound conditions

1. ## Compound conditions

Let A, B and C be conditions which can be either true or false. Suppose we want to writea computer program in which a certain piece of code should be executed if exactly one of thetwo conditions A and B is true, and in addition C is false. Using the operations ^, and ¬,write down a compound condition which is true only under the described circumstances. Usea truth table to prove that your expression has the required property.

To solve this I understand A can be True , then B would be False and also C would be False .
Or B can be True and then A would be False as would C be False.

A B C
T F F
F T F

I'm kind of not sure how to use the operations to make the compound condition .
Any help would be appreciated .
Thanks

2. ## Re: Compound conditions

Would I have to make 8 of each letter ?

A B C
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F ..... and from here try work out the compound condition?

3. ## Re: Compound conditions

I think I just figured it out to suit those conditions
is the compound condition (p ^ q) ∨ ¬ r
Am I right ?
Also is there any good tips to finding what operations to use in questions such as these?
Thanks

4. ## Re: Compound conditions

Originally Posted by bee77
Let A, B and C be conditions which can be either true or false. Suppose we want to writea computer program in which a certain piece of code should be executed if exactly one of the two conditions A and B is true, and in addition C is false. Using the operations ^, ∨ and ¬,write down a compound condition which is true only under the described circumstances. Use a truth table to prove that your expression has the required property.
The conditional is If $(A\wedge \neg B\wedge \neg C)\vee(\neg A\wedge B\wedge \neg C)$ then $\cdots$

5. ## Re: Compound conditions

(A^ ¬B ^ ¬C) ∨ (¬A^B^¬C)
(A and not B and not C) or (not A and B and not C)
then
¬(¬A^B^C) ∨ ¬(A^¬B^¬C)
I'm probably wrong ...sorry struggle with this

6. ## Re: Compound conditions

Originally Posted by bee77
(A^ ¬B ^ ¬C) ∨ (¬A^B^¬C)
(A and not B and not C) or (not A and B and not C)
then ¬(¬A^B^C) ∨ ¬(A^¬B^¬C)
Why did you add the part is red?
You were correct up to that point. But the red part is totally wrong. It has no meaning for the question.

If you wanted to simplify $(A\wedge \neg B\wedge \neg C)\vee(\neg A\wedge B\wedge \neg C)$
it could be $[(A\wedge \neg B)\vee(\neg A\wedge B)]\wedge\neg C$

You need to learn LaTeX coding. (A\wedge \neg B\wedge \neg C)\vee(\neg A\wedge B\wedge \neg C) between \$\$ gives the above.

7. ## Re: Compound conditions

Oh I thought I had to break it down further.
I assumed when you typed then... that it meant i had to go further ...sorry
The help with these problems is greatly appreciated .
Thanks again Plato !!

8. ## Re: Compound conditions

I also have no idea how you guys are so quick with this stuff ...0.o It takes me a while to do an example such as the above ...do i just simply follow the worded and or and not pars and slot them straight into the equation? I think i tend to over think...sigh

9. ## Re: Compound conditions

Originally Posted by bee77
I also have no idea how you guys are so quick with this stuff ..
Don't feel bad. Although I am now retired, I did teach courses in foundation of mathematics and topology for thirty-five years.

10. ## Re: Compound conditions

I wish I had your brain this logic course is hard for me ...as a mature age student back at uni