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1. My Dog Dylan loves being brushed. At the moment, he is not a happy doggie, so I can't have just brushed him.

If X, then Y => Not Y, then Not X
if I brush my Dog, he will love it => He is not happy, I can't have brushed him
CORRECT LOGIC.

2. Dylan barks loudly when he is alarmed or frightened. One night I woke up when he barked fiercely. I concluded that he must have been either alarmed or frightened, so I tiptoed down the stairs expecting to find a burglar in the house. Was my conclusion a logical one?

When Dylan is alarmed or frightened ==> Dylan barks loudly
Dylan barked loudly ==> alarmed or frightened.

Wrong Logic

Correct logic is :
If X, Then Y ==>
a) X then Y or
b) Not Y, Not X

1. Whenever the red light is on and the green light is off, it means that the protection shields are no longer in place covering the uranium core. The protection shields are covering the uranium core, yet the green light is off. This means that the red light must be off also.

Logic:
(A)
If a, then b => Not b, Not a

(B)
If Not(X and Y) ==> (X is true, Not Y) or (Y is true, Not X): Correct Logic
If Not(X and Y) ==> (X is Not true, Y true) or (Y is Not true, X): Wrong Logic

So, in the question:
(red is on) and (green is off) ==> (No Protection shield)
using (A)
(There is Protection shield) ==> Not((red is on) and (green is off))

Now we have for second Part (using B):
Not((red is on) and (green is off)) ==> (green is off), (red is off) [x, not y]
So logically Correct.

2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
No birds are mammals.
=> X (no birds) -> Y(mammals)
=> No Y [no (mammals)] -> No X [no (no birds)]
=> no mammals -> birds
Logically Correct.

3. Our leisure centre had a budget of Â£100,000 last year to be spent on a swimming pool costing Â£60,000 or a gymnasium costing Â£55,000. We went ahead and ordered the swimming pool to be built. Therefore we did not spend any money on having a gymnasium built last year.
Logic:
(X or Y) == Not(X and Y) => (X is true, Not Y) or (Y is true, Not X): Correct Logic
(spent 60k on swimming pool) or (spent 55k in gymnasium) => (spent 60k on swimming pool), Not (spent 55k in gymnasium)
So statement is Logically correct

Re: If X then Y, Help for CR [#permalink]
03 Jun 2005, 15:38

HongHu wrote:

Since we have been working on some logical reasoning questions I'm going to try to collect the principles I'm following here for everybody's reference. Please feel free to discuss and add more.

If X then Y This is the equivalent of: If non Y then non X. Example: If it rains, then I will take an umbrella with me. I don't have a umbrella with me. That must mean it is not raining.

This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y occurred, X may or may not happen. Example. If it rains, then I will definitely take an umbrella with me. I have a umbrella with me today. Is it raining? It may or may not be raining. I said if it rains I will take an umbralla with me. But I could also take an umbralla with me just for the sake of it, even if it doesn't rain. By the same token, if it is not raining, do I have an umbralla with me? I may or may not have.

I didn't Understand this.
First, You said that 'if it rains, then I will take an umbrella with me.' The 'If/then' here is a condition that implies that you will take an umbrella "only" if it is raining. Does GMAT have such devious logic?

Is there a way out for solving these syllogism problems with the help of Venn diagram?
I have heard it is.
Will any of the experts enlighten on this please?

Is there a way out for solving these syllogism problems with the help of Venn diagram? I have heard it is. Will any of the experts enlighten on this please?

Positive Negative

Universal All No

Particular Some Some........not

1) Some A's are not B's means atleast 1 A is not a B

2) All A's are B's means All B's are A's

3) A positive + A positive = always is a positive conclusion

4) A positive + a negative= Always leads to a negative conclusion

5) a negative + a Negtive = leads to no conclusion

6) A universal + a universal statement always gives the followin conclusions- either universal/a particular/a no conclision

7) a universal Conclusion+particular conclusion =always gives a particular conclusion

8) a particular + a particular = no conclusion

9) All A's are B's
All B's are C's
the conclision is exists = All C's are A's and vice versa

10) Some A's are C's
Some C's are A's = a conclusion cannot be derived...................

All A's are B's means that A->B is distributed But B-> A is not distributed

Some A's are B's means A->B is not ditributed nor is B->A distributed

No A's are B's means A->B is not true and B->A is not true . So here both
A and B are Distributed

11) All A's are B's
All C's are B's
No conclusion since the middle term B is not distributed in both

For a conclision to exist the middle term needs to be distributed atleast once.................................

12) All A's are B's
All A's are c's
Conclusion is Some B's are C's or vice versa

14) All A's are B's
Some A's are C's
Some b's are C's and vice versa

13) All A's are B's
Some B's are C's
No conclusion since B is not distributed......................

15) No A's are B's
Some A's are not C's
No conclusion since both premises are negative

16) many A's are b's
All b's are not C's
conclusion is some a's are not c's and vice versa

17)All a's are b's
No b's are c's
conclusion :No a's are c's and vice versa.....................

18) All a's are b's
All b's are c's
Conclision exists as b is distributed once............All a's are c's and vice versa. Some a's are c's and vice versa is also right.......

19) All a's are b's
All c's are b's
consluaion: No conclusion since the term b is not distributed

20) All a's are b's
All a's are c's
conclusion: Some b's are c's and vice versa

21) All a's are b's
Some a's are c's
conclusion : Some b's are c's

22) All a's are b's
Some b's are c's
Conslusion: No conclusion since b is not distributed at all...........

23) Many a's are b's
No b's are c's
Conclusion: Some a's are nto c's

24)No a's are b's
some a's are not c's
conlusion: No concluaion sonce both premises are negative

All+All = All /some
All+Some = Some
All+No= No/Some not
No+Some = Some not

Thanks HongHu for the awesome post.
And guys,these things are actually tested on the GMAT in one way or the other.
So, make sure u have a good hold of these concepts.

I have personally found using variable and mapping arguments to be very effective in understanding CR questions. Can anyone point me in the direction of some books or other sources that will help me get a better understanding of this concept?