Logic question Forum

[kovacs]

Hi everyone,

I'm reading PowerScore Logic Games Bible, and I am a bit puzzled.

From what I learned, doesn't "if N, then -A or -B" = "if N, then -(A and B)"?

But, it seems like PowerScore is saying "if N, then -A; and, if N, then -B" which is completely different than -(A and B) = not A and B together, but this still includes the possibility of either A or B being with N.

If you're curious as to the exact question, it's Game #1: October 1996 Questions 6-12 on pg. 117 of the PowerScore book.

Am I reading it wrong, and I am right, or have I learned the wrong material? Please help!

[merc280]

Hi everyone,

I'm reading PowerScore Logic Games Bible, and I am a bit puzzled.

From what I learned, doesn't "if N, then -A or -B" = "if N, then -(A and B)"?

But, it seems like PowerScore is saying "if N, then -A; and, if N, then -B" which is completely different than -(A and B) = not A and B together, but this still includes the possibility of either A or B being with N.

If you're curious as to the exact question, it's Game #1: October 1996 Questions 6-12 on pg. 117 of the PowerScore book.

Am I reading it wrong, and I am right, or have I learned the wrong material? Please help!

i believe its if A and B then N.

[glucose101]

Ya. It's A&B-->not N

[kovacs]

Ya. It's A&B-->not N

Then POWERSCORE IS WRONG?????

They clearly say that it's "if not N, then Not A and Not B"! That's completely different! Can someone please explain to me?? I will write it out below:

A university library budget committee must reduce exactly five of eight areas of expenditure -- G, L, M, N, P, R, S, and W -- in accordance with the following conditions:

If both G and S are reduced, W is also reduced.
If N is reduced, neither R nor S is reduced.
If P is reduced, L is not reduced.
Of the three areas, L, M, and R, exactly two are reduced.

EXCERPT from their analysis:

The second rule bears further analysis. When N is reduced, neither R or S is reduced, and it can be inferred from the contrapositive that when R or S is reduced, N cannot be reduced. Thus, N and R cannot be reduced together, and N and S cannot be reduced together. Consequently, we have written the rule in two separate parts to fully capture this powerful information.


Now, my contention is with the interpretation of the second line condition: If N is reduced, neither R nor S is reduced.
So, the negative of "not R or not S" is "R or S"? I thought it was "R and S" and "Not (not R or not S)".

Would someone please clarify the inference for me? Please!

[KevinP]

If N is reduced, neither R nor S is reduced.

The English usage of nor might throw you off. In Logic, A nor B means ~(a OR b) = ~a AND ~b. This might seem a bit counterintuitive.

So, N -> ~(R OR S)
Via De Morgan's law:
N -> ~R AND ~S

Contrapositive:
~(~R AND ~S) -> ~N
R OR S -> ~N

Edit: I think you had it as N -> ~R or ~S, which is wrong. N -> ~R AND ~S is correct.
https://secure.wikimedia.org/wikipedia/ ... ogical_NOR

[kovacs]

If N is reduced, neither R nor S is reduced.

The English usage of nor might throw you off. In Logic, A nor B means ~(a OR b) = ~a AND ~b. This might seem a bit counterintuitive.

So, N -> ~(R OR S)
Via De Morgan's law:
N -> ~R AND ~S

Contrapositive:
~(~R AND ~S) -> ~N
R OR S -> ~N

Thanks, Kevin! So, just to be clear, "Neither A nor B" translates as ~(a or b); whereas, "Not A or not B" translates as ~A or ~B. In other words, the use of the word "nor" always indicates the negative of the parenthetically enclosed disjunctive. Do the LSAT questions always use this format?

[KevinP]

Thanks, Kevin! So, just to be clear, "Neither A nor B" translates as ~(a or b); whereas, "Not A or not B" translates as ~A or ~B. In other words, the use of the word "nor" always indicates the negative of the parenthetically enclosed disjunctive. Do the LSAT questions always use this format?

Yes. NOT A or NOT B = ~A or ~B. And yes, NOR always indicates that ~(a OR b) = ~a AND ~b. In logic, words such as AND, OR, NOR etc. have very specific definitions and LSAC always adheres to them.

However, I do find myself going WTF sometimes if LSAC words thing really weirdly. They'll still use the precise definition of logical terms, it's just they'll add unnecessary words to try and confuse me.

Edit, if this helps:
If N is reduced, neither R nor S is reduced: N -> ~R AND ~S
If N is reduced, either R or S is not reduced: N -> ~R OR ~S

[kovacs]

Thanks so much, Kevin! This'll save me from getting at least 5 wrong questions! Now I know better.

[kovacs]

Just to be clear, just as "nor" is a trigger for a ~(A or B) statement, does "neither" trigger the same logical format as nor?

[tomwatts]

Just to be clear, just as "nor" is a trigger for a ~(A or B) statement, does "neither" trigger the same logical format as nor?

Yes. Given that "neither" is hard to use without using "nor" right after, this is sort of redundant, but yes, in case someone says something like "neither of them."

[kovacs]

Just to be clear, just as "nor" is a trigger for a ~(A or B) statement, does "neither" trigger the same logical format as nor?

Yes. Given that "neither" is hard to use without using "nor" right after, this is sort of redundant, but yes, in case someone says something like "neither of them."

Thanks!