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09 Apr 2005, 22:25
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Describe what logical pattern is used and whether it is valid one?
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.
2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
3. Our leisure centre had a budget of £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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.
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.
2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
3. Our leisure centre had a budget of £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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.
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10 Apr 2005, 08:49
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This is what I think, although I'd appreciate some other thoughts on it...
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 X+Y, then Z. Since not Z, there cannot be X+Y. Since there are a set of conditions that need to be in place, this is a logical conclusion.
2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
A is not B, therefore B is not A. This logic is flawed, if you consider a rectangle is not a square (A is not B), but a square is a rectangle (B IS A).
3. Our leisure centre had a budget of £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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.
They can pick either A OR B (according to the question). If they chose A, then they couldn't choose B. Of course, that doesn't mean that they couldn't have put money towards a gymnasium. I'm not sure...
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 X+Y, then Z. Since not Z, there cannot be X+Y. Since there are a set of conditions that need to be in place, this is a logical conclusion.
2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
A is not B, therefore B is not A. This logic is flawed, if you consider a rectangle is not a square (A is not B), but a square is a rectangle (B IS A).
3. Our leisure centre had a budget of £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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.
They can pick either A OR B (according to the question). If they chose A, then they couldn't choose B. Of course, that doesn't mean that they couldn't have put money towards a gymnasium. I'm not sure...
11 Apr 2005, 17:02
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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 £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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
Banerjee, Honghu, Anand, Paul, others. Please comment on my above answers whether they are correct.
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 £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £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
Banerjee, Honghu, Anand, Paul, others. Please comment on my above answers whether they are correct.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Critical Reasoning (CR) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
