CRE 2 - Negation of Statements | LR - Logical Connectives
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Answer the next 10 questions based on the information given.
Each question given below is a statement followed by four different statements. Choose the one which is the correct negation of the given statement.
Either Vishal or Akash will be the president.
- (a)
Vishal is not the president, so Akash is the president
- (b)
Neither Vishal nor Akash is the president
- (c)
Akash is not the president but Vishal is the president
- (d)
None of these
Answer: Option B
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Explanation :
Here,
p = Vishal is the president.
q = Akash is the president.
Statement: Either p or q
Negation:
~(p or q) = ~p and ~q
Hence, option (b).
Workspace:
Whenever Nutan and Palak go to parlor, Himanshi follows them.
- (a)
Himanshi follows Nutan and Palak but they are not going to parlor.
- (b)
Nutan and Palak are going to parlor and Himanshi follows them.
- (c)
Himanshi does not follow Nutan and Palak even when they go to parlor.
- (d)
None of these
Answer: Option C
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Explanation :
Here,
p = Nutan and Palak go to the parlor.
q = Himanshi follows them.
Statement: If p, q
i.e., p ⇒ q.
Negation: p and ~q.
i.e., Nutan and Palak go to the parlor and Himanshi does not follow them.
Hence, option (c).
Workspace:
Ankush will go to school, only if his stomach is full.
- (a)
Ankush is not going to school even when his stomack is full.
- (b)
Ankush’s stomach is not full but he went to school.
- (c)
Ankush is not going to school because his stomach is not full.
- (d)
None of these
Answer: Option B
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Explanation :
Here,
p = Stomach is full.
q = Ankush is going to school.
Statement: Only if p, q.
i.e., q ⇒ p
Negation: q and ~p.
Hence, option (b).
Workspace:
Unless Bindu plays guitar, Geeta will not play piano.
- (a)
Geeta is not playing piano, but Bindu is playing guitar.
- (b)
Bindu is playing guitar, Geeta is playing piano.
- (c)
Geeta is playing piano but Bindu is not playing guitar.
- (d)
None of these
Answer: Option C
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Explanation :
Here,
p = Bindu is playing guitar.
q = Geeta is not playing piano.
Statement: Unless p, q
i.e., ~p ⇒ q
Negation: ~p and ~q.
Hence, option (c).
Workspace:
Unless the change happens, the problem will not be solved.
- (a)
The problem is solved and the change did not happen.
- (b)
The change happened but the problem is not solved.
- (c)
The change happened and the problem is solved.
- (d)
The problem is solved implies, the change happened.
Answer: Option A
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Explanation :
Here,
p = Change happens.
q = Problem is not solved.
Statement: Unless p, q
i.e., ~p ⇒ q
Negation: ~p and ~q.
Hence, option (a).
Workspace:
The play was long but entertaining.
- (a)
The play was not long and not entertaining.
- (b)
The play was long but not entertaining.
- (c)
The play was not long or not entertaining.
- (d)
The play was entertaining but not long.
Answer: Option C
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Explanation :
Here,
p = Play was long.
q = Play was entertaining.
Statement: p and q
Negation: ~(p and q)
∴ ~p or ~q
Hence, option (c).
Workspace:
Unless Hardik learns driving, he cannot go on the roadtrip.
- (a)
Hardik learned driving but he could not go on roadtrip.
- (b)
Hardik did not learn driving, but he went on a roadtrip.
- (c)
Hardik learned driving and went on roadtrip.
- (d)
Hardik did not learn driving and he did not go on roadtrip.
Answer: Option B
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Explanation :
Here,
p = Hardik learns driving.
q = Hardik does not go on roadtrip.
Statement: Unless p, q
i.e., ~p ⇒ q
Negation: ~p and ~q.
Hence, option (b).
Workspace:
He either starts a business or he will join a job.
- (a)
He started a business and did not join a job.
- (b)
He started a business but joined a job.
- (c)
He did not start a business and joined a job.
- (d)
He did not start a business and did not join a job.
Answer: Option D
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Explanation :
Here,
p = He starts a business.
q = He joins a job.
Statement: Either p or q
Negation:
~(p or q) = ~p and ~q
Hence, option (d).
Workspace:
If you speak well, you will become celebrity.
- (a)
You don’t speak well and you are a celebrity.
- (b)
You speak well but you are not a celebrity.
- (c)
You don’t speak well and you are not a celebrity.
- (d)
You speak well so you are a celebrity.
Answer: Option B
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Explanation :
Here,
p = You speak well.
q = You are a celebrity.
Statement: If p, q
i.e., p ⇒ q.
Negation: p and ~q.
Hence, option (b).
Workspace:
The class will go on a filed trip, only if everyone passes the exam.
- (a)
Class went on a trip when everyone passed the exam.
- (b)
Class did not go on the trip because not everyone passed the exam.
- (c)
Class went on the trip even through not everyone passed the exam.
- (d)
Class did not go on the trip even when everyone passed the exam.
Answer: Option C
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Explanation :
Here,
p = Everyone passed the exam.
q = Class went on the trip.
Statement: Only if p, q.
i.e., q ⇒ p
Negation: q and ~p.
Hence, option (c).
Workspace:
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