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Yeah if they BOTH occur B must occur.

Thats what the contrapositive says.

StrictlyLiable wrote:Yeah if they BOTH occur B must occur.

Thats what the contrapositive says.

And if NEITHER of them occur, then B must occur as well. Sort of a double contrapositive as a result of the "but not both".

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dakatz wrote:

StrictlyLiable wrote:Yeah if they BOTH occur B must occur.

Thats what the contrapositive says.

And if NEITHER of them occur, then B must occur as well. Sort of a double contrapositive as a result of the "but not both".

Yeah, I get that. So there's a double contrapositive with "but not both" statements? WOW, I never know that. Thanks!!!

ly2010 wrote:

StrictlyLiable wrote:Yeah if they BOTH occur B must occur.

Thats what the contrapositive says.

I must be retarded with these either or statements.
If Not B, then H or I.
If not H and not I, then B. (contrapositive)

I guess if I didn't draw it out it makes sense that if both occur, B must occur, but isn't the contrapositive saying that if you don't have H or I, then you have B?

Oh maybe "If B does not occur, then either H or I but not both occur" is really "Not B->Not H or Not I" because then contrapositive would be If I and H then B.

Here is how to read the overall statement:

"If Not B, then H or I, but not both must occur"

"If it is not the case that you have H or I but not both, then you have B"

That contrapositive can be fulfilled by either having both H and I, or having neither of them.

ly2010 wrote:I'm doing a Pure Grouping Drill and I'm a little confused by the answer TM provided. I might be reading it wrong...

The statement says: "If B does not occur, then either H or I but not both occur."

Does this mean that if both H and I occur, then B also occurs? (That's what the answer is telling me)

I interpreted it as, "If not B, then H or I." and "If not H and not I, then B"

Thanks!

It means that if no B then:

A. H occurs, I does not
B. I occurs, H does not
C. H & I both do not occur.

Don't forgot about scenario C!


I wouldn't worry about the contrapositive for this one, it's fairly complex and most likely entirely unnecessary since you'd need to make 2 separate contrapositive that correspond to either H or I and not H and not I. I could be wrong on this, someone correct me if I'm wrong.


Also as I'm sure as you know, if the rule was If B does not occur, then either H or I

Then it would be:
a. H occurs, I does not.
b. I occurs, H does not.
c. Both I and H occur

Contrapositive:

If H and I do not occur--> B occurs

Either or is much easier to work with than "but not both," especially w/ contrapositives.


Hope that helps!

Yeah, I get the logical behind but I don't know how the diagram works unless I am writing two out. I'm doing the TM Pure Grouping Drill so I'm being stubborn and trying to make sure I can diagram everything out. I think during the test, when I get "but not both" statements, I'll just think about it and not write it out.

Anaconda wrote:

ly2010 wrote:I'm doing a Pure Grouping Drill and I'm a little confused by the answer TM provided. I might be reading it wrong...

The statement says: "If B does not occur, then either H or I but not both occur."

Does this mean that if both H and I occur, then B also occurs? (That's what the answer is telling me)

I interpreted it as, "If not B, then H or I." and "If not H and not I, then B"

Thanks!

It means that if no B then:

A. H occurs, I does not
B. I occurs, H does not
C. H & I both do not occur.

Don't forgot about scenario C!


I wouldn't worry about the contrapositive for this one, it's fairly complex and most likely entirely unnecessary since you'd need to make 2 separate contrapositive that correspond to either H or I and not H and not I. I could be wrong on this, someone correct me if I'm wrong.

Hope that helps!

Its simple to remember. If the statement's says "or", it will say "and" in the contrapositive and vice versa. If A occurs, then B or C occurs, but not both. Contrapositive: If B and C do not occur, then A does not occur.

Another example: If A occurs, then B and C occur. Contrapositive: If B or C do not occur, A does not occur.

Thank you Powerscore! Lets hope this knowledge comes in handy on test day. I feel like all the crap we learn from books wont do sh*t come test day. Ha!

Yeah, I totally know what you mean. I think I figured the diagram out actually. If there is a "but not both" you can't make just one diagram. It is possible that neither H or I occur so you have to write: If not B then Not H and Not I. That contrapositive is then "if I and if H then B"

Thanks for all the help guys!!!

gdane5 wrote:Its simple to remember. If the statement's says "or", it will say "and" in the contrapositive and vice versa. If A occurs, then B or C occurs, but not both. Contrapositive: If B and C do not occur, then A does not occur.

Another example: If A occurs, then B and C occur. Contrapositive: If B or C do not occur, A does not occur.

Thank you Powerscore! Lets hope this knowledge comes in handy on test day. I feel like all the crap we learn from books wont do sh*t come test day. Ha!