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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
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.
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.
If a, then b => Not b, Not a
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)
(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
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.
(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
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?
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?