Discrete math

[Albi]

Hello, can you help me with the following problem.Problem 43.What should I do next?

 

[Steven G]

Please think about it and give it a try. Then post back with your reasoning.

When is p or q or r true? When is -p or -q or -r true?

 

[Albi]

Please think about it and give it a try. Then post back with your reasoning.

Did you see the image

 

[Steven G]

I think that your teacher wants the answers in words. And yes I did see your work.

 

[Albi]

I think that your teacher wants the answers in words. And yes I did see your work.

We can conclude that for(p v q v r) to be true at least one p,q,r needs to be true.and for the other proposition at least one p,q or r needs to be false.

 

[Albi]

We can conclude that for(p v q v r) to be true at least one p,q,r needs to be true.and for the other proposition at least one p,q or r needs to be false.

But I want to find the values of p,q and r.

 

[pka]

Hello, can you help me with the following problem.Problem 43.What should I do next?

I found that the directions are confusing.
Here is my take: We are to explain, without truth-tables, why if at least one of \(p,~q,\text{ or }r\) is true and at least one of \(p,~q,\text{ or }r\) is false then \((p\vee q\vee r)\wedge (\neg p\vee\neg q\vee\neg r)\) is true. If \(p\) is true then \((p\vee q\vee r)\) is true.
If \(q\) is false then \(\neg q\) is true so \((\neg p\vee\neg q\vee\neg r)\) is also true since both are true we have
\((p\vee q\vee r)\wedge (\neg p\vee\neg q\vee\neg r)\) is true, when we assume one variable is true and one false.