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Has anyone learned about logical proofs before? It looked pretty simple on the blackboard, but now that I'm actually trying it, its MAD CONFUSING!!!!

Here's the question

A -> B
~(C^B)
C
__________
~A

Can someone tell me where to start or at give me a website about it? THANKS!!!

2006-10-11 14:25:06 · 3 answers · asked by Anonymous in Science & Mathematics Mathematics

3 answers

~ means "not"
^ means "and"
v means "or"
-> means "then" or "implies"

First remember that A -> B is equivalent to ~A v B, as shown below:

A . B . ~A . (A -> B) . (~A v B)
F . F ... T ........ T .......... T
F . T ... T ........ T .......... T
T . F ... F ........ F .......... F
T . T ... F ........ T .......... T

Also ~(C ^ B) is equivalent to ~C v ~B (by DeMorgan's law). You can prove this by creating a table as shown above, or just use it. When you distribute the ~ through, remember to flip the ^ (and) to v (or).

So you have the following equivalent set of statements:
~A v B
~C v ~B
C

It's always easiest to start with the line that only has one value, namely #3. This means that C is true.

Now look at #2. Because C is true, ~C is false, therefore ~B must be true to make the statement true.

Finally look at #1. B is false (because ~B was shown true above). Again ~A must be true to make the statement true.

Thus ~A is true, as was to be proven.

2006-10-13 05:04:20 · answer #1 · answered by Puzzling 7 · 0 0

A -> B is the same as ~B -> ~A Law of Contrapostive

~(C and B) is the same as ~C or ~B DeMorgan's Law

Since C is True, ~B Must be true and thus ~A must be true, since ~B -> ~A

2006-10-11 14:34:38 · answer #2 · answered by z_o_r_r_o 6 · 3 1

i like ur avatar

2006-10-11 14:32:25 · answer #3 · answered by cw 1 · 0 1

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