2

Wed 29 Apr, 2015 08:28 pm
1. ~A>~B
A>C
Z>W
~C*~W Conclusion: /~B v W

2. P>(Q>(R v S))
P*Q
S>T
~T v ~W
~~W Conslusion: /R

3. (A*B)>~C
C v ~D
A>B
E*A Conclusion: /~D

4. B>E
E>(C*S)
~S
B Conclusion: /C

Please help me, I don;t understand these to save my life! And have a big exam on them.
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Type: Question • Score: 2 • Views: 1,475 • Replies: 6
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layman

0
Wed 29 Apr, 2015 09:09 pm
@mackenziec,
You'll never understand any of it until you understand the meaning of the symbols used. Do you? I don't--if this is standard "terminology" for symbolic logic, then I' ve forgotten it. Can you translate these symbolic "sentences" in words?

For example, I would translate "S>T" as saying "S is larger than T" in standard English. How about the rest of it?
mackenziec

1
Wed 29 Apr, 2015 09:31 pm
@layman,
The > stands for then
The * stands for and
The v stands for or
FBM

1
Wed 29 Apr, 2015 09:32 pm
@mackenziec,
mackenziec wrote:

1. ~A>~B
A>C
Z>W
~C*~W Conclusion: /~B v W

2. P>(Q>(R v S))
P*Q
S>T
~T v ~W
~~W Conslusion: /R

3. (A*B)>~C
C v ~D
A>B
E*A Conclusion: /~D

4. B>E
E>(C*S)
~S
B Conclusion: /C

Please help me, I don;t understand these to save my life! And have a big exam on them.

Do you want them translated into text or checked for validity? Truth tables? What exactly do you need?

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layman

1
Wed 29 Apr, 2015 09:35 pm
@mackenziec,
0 Replies

fresco

2
Thu 30 Apr, 2015 01:08 am
@mackenziec,
These are logical arguments for which you are being asked to test the validity. Each line prior to the conclusion represents a separate premise and the premises are conjoined . An easy way (not involving full truth tables) is sometimes called "the method of backward fell swoop" (ref Quine) in which you take the truth value of the conclusion to be false and show how this would make the premises false. You must however learn the four basic truth tables ( for conjunction, disjunction, negation and implication) in order to do this exercise.
For example in no.4, assume C =0 (false), this would make E=0 in the second line, which would make B=0 in the first line. Then the fourth line which implies B=1 would be a contradiction. So validity has been proved since C=1 is the only way to avoid a contradiction.
0 Replies

fresco

1
Thu 30 Apr, 2015 11:56 am
@mackenziec,
NB Alternatively this explains the full truth table method.
0 Replies

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