Pure Grouping Question Forum

[ly2010]

.

[StrictlyLiable]

Yeah if they BOTH occur B must occur.

Thats what the contrapositive says.

[dakatz]

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".

[ly2010]

.

[ly2010]

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!!!

[dakatz]

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.

[Anaconda]

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!

[ly2010]

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.

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!

[gdane]

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!

[ly2010]

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!!!

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!