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#1 2009-06-02 03:35:22
- karney
- Guest
discrete
Given that not (A and B) implies C, what does (not C) imply?
What is the best way to workthrough these types of problems? Thanks.
#2 2009-06-02 04:26:10
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: discrete
Use the law of the contrapositive.
Do you know what that is?
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#3 2009-06-02 17:24:31
- karney
- Guest
Re: discrete
Given that not (A and B) implies C, what does not (not C) imply? OK, lets see if I got this straight. Another way to say this would be that (A and B) imply C, so (C) implies A and B. So the answer is (not C) implies A and B. Correct?
#4 2009-06-02 20:30:35
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: discrete
The final answer is right, but the reasoning isn't.
The Law of Contrapositive says that if A ⇒ B, then (not B) ⇒ (not A).
Putting your implication into this gives (not C) ⇒ not(not(A and B) = (A and B)
However, the direction of an implication can't be reversed in general, so C ⇒ not(A and B) might not be true.
Why did the vector cross the road?
It wanted to be normal.
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