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Know the answer to these logic problems?
I'm working on logic homework, and I'm stuck on a few questions. (I did most of them; I'm not just trying to get someone else to do my work for me.) If you know any of them, and could explain them to me, I'd be incredibly grateful. I'll pick a best answer!
1. How many structures are possible for "not P and Q or R"?
(The answer is 1-5)
2. Given the following truth assignments:
P - true
Q - true
R - false
Is "If P and R, then Q" true or false?
3. Is P->((NOT P) -> Q) a contradiction, contraposition, or tautology?
4. Which statement is logically true?
- It is not the case that Sandy knows what happened yesterday, and neither does Mary. Therefore, according to De Morgan’s Law, Sandy or Mary knows what happened yesterday.
- I know John likes basketball or Jerry likes football. Therefore, there is a chance that John likes basketball and Jerry likes football.
5. From the perspective of propositional calculus, is the statement “If 2+5=7, then
Rome is the capital city of Surinam” true?
2 Answers
- VishalLv 61 decade agoFavorite Answer
1. I can only think of three, but it's possible that I may have missed one or two.
Not (P and Q) or R
(Not P and Q) or R
Not P and (Q or R)
2. The statement (P and R) --> Q is true if Q is true or if (P and R) is false. Since Q is true, the whole statement is true.
3. It's a tautology.
If P is true, then (not P) is false, which would make ((NOT P) -> Q) true regardless of whether or not Q is true. Any time the consequent of a conditional is true, the whole conditional is true, so if P is true the whole statement is true.
If P is false, then (P -> anything) is true, so the whole statement is true.
Since it is true regardless of whether or not P is true.
If you don't understand my explanation, this problem might be easier to explain to yourself using truth tables. Just make a truth table for the entire statement and you'll see that the statement as a whole comes out true every time.
4. The second statement is true. The first one is false because De Morgan's Law says that (not S and not M) is logically equivalent to (not (S or M)), and the statement leaves out a 'not.'
5. No, it is false. For a conditional to be false, you need the antecedent to be true and the consequent to be false. Since 2+5=7 is true and "Rome is the capital city of Surinam" is false, the statement is false.
- 1 decade ago
For number four, it's the bottom answer.
It's like, if I know I have a quarter in my left and OR a penny in my right hand, it's still possible that I have a quarter in my left hand AND a penny in my right.
And that's about all I can do. Sorry, maybe you could explain calculus to me one day.
