Finite Homework Help

[Dizzy's]

My friend whom I work with is taking finite math (summer school) and she asked me if i could take a look at her homework for her. I have taken up to calculus, I didn't know she was asking for help on finite, so I figured that i would give it a shot. I will post the questions and give what I think the answer is.

1.) Let p represent the statement “It is Thursday” and let q represent the statement “I have a quiz today.” Which of the following represents the symbolic statement p ∧¬q ?

It is Thursday and I don’t have a quiz today

2.) Which of the following is the correct truth table for ¬p ∨ q ?

p q ¬p ∨ q
T T T
T F F
F T T
F F T

3.) Based on the answer to the previous question, which of the following is logically equivalent to ¬p ∨ q ?

p ∧ q

4.) Which of the following is the correct truth table for ¬ ( q → p ) ?

p q ¬ ( q→ p )
T T F
T F T
F T F
F F F

5.) Which of the following are the correct first four rows of the truth table for p ∨ ( q ↔ r ) ?

p q r p ∨ ( q ↔ r )
T T T T
T T F T
T F T T
T F F T

6.) Which of the following are the correct second four rows of the truth table for p ∨ ( q ↔ r ) ?

p q r p ∨ ( q ↔ r )
F T T T
F T F F
F F T F
F F F T

7.) Is p ∨ ( p ∧ q ) a tautology?

Yes

8.) Which of the following is logically equivalent to p ∨ ( p ∧ q ) ?

p ∨ q

The help is much appreciated.

[Greatguardian]

3 is wrong, 4 is wrong, 7 is wrong, 8 is wrong.

I'm not sure if you wanted to just check your answers or if you wanted a bit more than that. Though I'm also not sure how I can really explain some of them without just giving away the answers (I have no qualms with this, but I'll avoid it unless it's asked for), since this is pretty basic propositional logic.

[Cayos]

For 3, look up De Morgan's Law.
For 4, use De Morgan's and also look up the logical equivalence of q implies p.
For 7, a truth table would work best. Also, look up Distributive Law, Idempotent Law, and Complement Law. Are you always going to get T, no matter what you substitute in to p and q? Look up the definition of a tautology
For 8, Use Distributive Law.


You can find pretty much all of this information on the discrete math wiki page. I think you'll find the section at the bottom on "Laws of Logic" the most useful.

http://en.wikibooks.org/wiki/Discrete_Mathematics/Logic

[Dizzy's]

Thanks for the help, it was not for me it was for a friend. I have never taken finite so i have little to no idea what im doing where thats concerned. I only took up to calculus, i offered to help not knowing what class she was in first.