CRE 3 - 3 Statements | LR - Logical Connectives
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Answer the next 5 questions based on the information given below:
Each question below consists of a main statement followed by four numbered statements. From the numbered statements, select the one that logically follows the main statement.
If it is a Sunday, then I will go to a movie or I will read a novel.
- (a)
It is not a Sunday, implies that I am not going to a movie and I am not reading a novel.
- (b)
It is a Sunday and I am not reading a novel means that, I am watching a movie.
- (c)
I am not watching a movie and I am reading a novel, means that it is a Sunday.
- (d)
None of these
Answer: Option B
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Explanation :
Here,
p = It is Sunday.
q = I go to a movie.
r = I read a novel.
Statement: If p, (q or r)
Conclusion 1: p ⇒ (q or r)
(i) p and ~q ⇒ r
(ii) p and ~r ⇒ q
Conclusion 2: ~(q or r) ⇒ ~p
∴ ~q and ~r ⇒ ~p
Option (b) corresponds to conclusion 1 (ii).
Hence, option (b).
Workspace:
Unless it is a holiday and Manoj has money, he cannot go for movie.
- (a)
Manoj is going for the movie, hence, he has money but it is not a holiday.
- (b)
Manoj is going for the movie, implies that it is a holiday but he does not have money.
- (c)
Manoj does not have money implies, he is not going for movie.
- (d)
More than one of the above
Answer: Option C
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Explanation :
Here,
p = It is a holiday.
q = Manoj has money.
r = He is not going for the movie.
Statement: Unless (p and q), r
Conclusion 1: ⇒ ~(p and q) ⇒ r
(i) ~p ⇒ ~r
(ii) ~q ⇒ ~r
Conclusion 2: ~r ⇒ p and q
Option (c) corresponds to conclusion 1 (ii).
Hence, option (c).
Workspace:
If Vikas is creative and energetic, he will be successfull.
- (a)
Vikas is creative implies that he will be successful.
- (b)
Vikash is energetic means, he will be successful.
- (c)
Vikas is not successful means that he is neither creative nor energetic.
- (d)
All of the above
Answer: Option D
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Explanation :
Here,
p = Vikas is creative.
q = Vikas is energetic.
r = Vikas is successful.
Statement: If (p or q), r
Conclusion 1: ⇒ (p or q) ⇒ r
(i) p ⇒ r
(ii) q ⇒ r
Conclusion 2: ~r ⇒ ~(p or q)
∴ ~r ⇒ ~p and ~q
Option (a) corresponds to conclusion 1 (i).
Option (b) corresponds to conclusion 1 (ii).
Option (c) corresponds to conclusion 2.
Hence, option (d).
Workspace:
If I study well, I will get admission into either IITs or NITs.
- (a)
I did not get admission into IITs or NITs implies that I did not study well.
- (b)
I did not study well means that I will get admission neither in IITs nor in NITs.
- (c)
I got admminsion into IITs or NITs means that I studied well.
- (d)
I did not get admission into IITs and NITs means that I did not study well.
Answer: Option D
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Explanation :
Here,
p = I studies well.
q = I got admission into IITs.
r = I got admission into NITs.
Statement: If p, (q or r)
Conclusion 1: p ⇒ (q or r)
(i) p ⇒ q and ~r
(ii) p ⇒ ~q and r
(iii) p ⇒ q and r
Conclusion 2: ~(q or r) ⇒ ~p
∴ ~q and ~r ⇒ ~p
Option (d) corresponds to conclusion 2.
Hence, option (d).
Workspace:
If it is a holiday, then I will play cricket and watch a movie.
- (a)
I did not play cricket or I did not watch a movie, means that it was not a holiday.
- (b)
It is not a holiday, means that I will not play cricket and I will not watch a movie.
- (c)
I played cricket and I watched a movie, means that it was not a holiday.
- (d)
I played cricket and I watched a movie, means that it was a holiday.
Answer: Option A
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Explanation :
Here,
p = It is a holiday.
q = I play cricket.
r = I watch a movie.
Statement: If p, (q and r)
Conclusion 1: p ⇒ (q and r)
Conclusion 2: ~(q and r) ⇒ ~p
∴ ~q or ~r ⇒ ~p
(i) ~q ⇒ ~p
(ii) ~r ⇒ ~p
Option (a) corresponds to conclusion 2.
Hence, option (a).
Workspace:
Unless you eat healthy, you will become obese and develop health issues.
- (a)
You did not eat healthy, you became obese and developed health issues.
- (b)
You did not develop health issues or become obese, implies that you did not eat healthy.
- (c)
You became obese and developed health isues implies that you did not eat healthy.
- (d)
You did not become obese but you developed health issues means that you did not eat healthy.
Answer: Option A
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Explanation :
Here,
p = Eat healthy.
q = become obese.
r = develop health issues.
Statement: Unless p, (q and r)
Conclusion 1: ⇒ ~p ⇒ (q and r)
Conclusion 2: ~(q and r) ⇒ p
∴ ~q or ~ r ⇒ p
(i) ~q ⇒ p
(ii) ~r ⇒ p
Option (a) corresponds to conclusion 1.
Hence, option (a).
Workspace:
If the cat is away, the mice will play or drink milk.
- (a)
The mice did not play or drink milk, implies that the cat is not away.
- (b)
If the cat is not away, the mice will neither play nor drink milk.
- (c)
The mice neither play nor drink milk, implies that the cat is not away.
- (d)
If the cat is not away, the mice will not play or not drink milk.
Answer: Option C
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Explanation :
Here,
p = cat is away.
q = mice will play.
r = mice will drink milk.
Statement: If p, (q or r)
Conclusion 1: p ⇒ (q or r)
(i) p and ~q ⇒ r
(ii) p and~r ⇒ q
Conclusion 2: ~(q or r) ⇒ ~p
∴ ~q and ~r ⇒ ~p
Option (c) corresponds to conclusion 2.
Hence, option (c).
Workspace:
Whenever it rains heavily, either it gets flooded or we get a pleasent weather.
- (a)
If the weather is pleasent or it is flooded, then it must have rained heavily.
- (b)
If the weather is not pleasent and it is not flooded, then it did not rain heavily.
- (c)
If it does not rain heavily, neither will it get flooded nor do we get a pleasent weather.
- (d)
If it rains heavily and we get a pleasent weather, then it will not get flooded.
Answer: Option B
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Explanation :
Here,
p = rains heavily.
q = it gets flooded.
r = we get pleasant weather.
Statement: If p, (q or r)
Conclusion 1: p ⇒ (q or r)
(i) p and ~q ⇒ r
(ii) p and~r ⇒ q
Conclusion 2: ~(q or r) ⇒ ~p
∴ ~q and ~r ⇒ ~p
Option (b) corresponds to conclusion 2.
Hence, option (b).
Workspace:
Whenever Australia plays England, I will either bite my nails or my BP rises.
- (a)
Australia is not playing England, means that I will neither bite my nails nor my BP does rise.
- (b)
I am biting my nails or my BP rises, implies that Australia is playing England.
- (c)
I am not biting my nails or my BP did not rise, means that Australia is not playing England.
- (d)
If Australia is playing England but my BP is not rising, means that I must be biting my nails.
Answer: Option D
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Explanation :
Here,
p = Australia play England.
q = I bite my nails.
r = my BP rises.
Statement: If p, (q or r)
Conclusion 1: p ⇒ (q or r)
(i) p and ~q ⇒ r
(ii) p and~r ⇒ q
Conclusion 2: ~(q or r) ⇒ ~p
∴ ~q and ~r ⇒ ~p
Option (d) corresponds to conclusion 1 (ii).
Hence, option (d).
Workspace:
Whenever inflation is on the rise, consumption will reduce and savings will increase.
- (a)
Consumption did not reduce or savings did not increase, means that the inflation is not on the rise.
- (b)
If consumption is not reduced but inflation is on the rise, then the savings will definitely increase.
- (c)
If consumption is reduced but savings does not increase, it means that the inflation is not on the rise.
- (d)
Both (a) and (c) above.
Answer: Option D
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Explanation :
Here,
p = Inflation is on the rise.
q = consumption reduces.
r = savings increase.
Statement: If p, (q and r)
Conclusion 1: p ⇒ (q and r)
Conclusion 2: ~(q and r) ⇒ ~p
∴ ~q or ~r ⇒ ~p
(i) ~q ⇒ ~p
(ii) ~r ⇒ ~p
Option (a) corresponds to conclusion 2 and option (c) corresponds to conclusion 2 (ii).
Hence, option (d).
Workspace:
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