Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > Consider the following two statements.S1: If ...
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Consider the following two statements.
S1: If a candidate is known to be corrupt, then he will not be elected
S2: If a candidate is kind, he will be elected
Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
S1: If a candidate is known to be corrupt, then he will not be elected
S2: If a candidate is kind, he will be elected
Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
- a)If a person is known to be corrupt, he is kind
- b)If a person is not known to be corrupt, he is not kind
- c)If a person is kind, he is not known to be corrupt
- d)If a person is not kind, he is not known to be corrupt
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following two statements.S1: If a candidate is known to b...
Concept:
Hypothetical syllogism,
If p → q and q → r then p → r
Formula:
p → q ≡ ¬ q → ¬ p ≡ ¬ p ∨ q
Hypothetical syllogism,
If p → q and q → r then p → r
Formula:
p → q ≡ ¬ q → ¬ p ≡ ¬ p ∨ q
Explanation:
C(x): x is known to be corrupt
E(x): x will be elected
K(x): x is kind
Statement S1 can be written as:
S1 ≡ C(x) → ¬E(x)
S2 can be written as:
S2 ≡ K(x) → E(x) ≡ ¬E(x) →¬K(x)
By using hypothetical syllogism,
From S1 and S2, the conclusion is
C(x) → ¬K(x) ≡ K(x) → ¬C(x)
If a person is kind, then he is not known to be corrupt.
C(x): x is known to be corrupt
E(x): x will be elected
K(x): x is kind
Statement S1 can be written as:
S1 ≡ C(x) → ¬E(x)
S2 can be written as:
S2 ≡ K(x) → E(x) ≡ ¬E(x) →¬K(x)
By using hypothetical syllogism,
From S1 and S2, the conclusion is
C(x) → ¬K(x) ≡ K(x) → ¬C(x)
If a person is kind, then he is not known to be corrupt.
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Community Answer
Consider the following two statements.S1: If a candidate is known to b...
Given Statements:
S1: If a candidate is known to be corrupt, then he will not be elected
S2: If a candidate is kind, he will be elected
To find:
Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
Answer:
The given statements can be represented as follows:
S1: Corrupt ⟹ ¬Elected (If a candidate is known to be corrupt, then he will not be elected)
S2: Kind ⟹ Elected (If a candidate is kind, he will be elected)
We need to find a statement that follows from both S1 and S2.
Explanation:
To find the statement that follows from both S1 and S2, we need to combine the given statements using logical operators.
If we take the contrapositive of S1, we get:
¬¬Elected ⟹ ¬Corrupt (If a candidate is elected, then he is not known to be corrupt)
Combining the contrapositive of S1 with S2, we get:
If a candidate is elected, then he is not known to be corrupt and is kind.
This statement can be written as:
Elected ⟹ (¬Corrupt ∧ Kind)
So, the correct answer is option C:
If a person is kind, he is not known to be corrupt.
This can be further explained by considering the following cases:
- If a person is corrupt, according to S1, he will not be elected. So, he cannot be kind.
- If a person is kind, according to S2, he will be elected. So, he cannot be known to be corrupt.
Hence, option C is the correct answer.
S1: If a candidate is known to be corrupt, then he will not be elected
S2: If a candidate is kind, he will be elected
To find:
Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
Answer:
The given statements can be represented as follows:
S1: Corrupt ⟹ ¬Elected (If a candidate is known to be corrupt, then he will not be elected)
S2: Kind ⟹ Elected (If a candidate is kind, he will be elected)
We need to find a statement that follows from both S1 and S2.
Explanation:
To find the statement that follows from both S1 and S2, we need to combine the given statements using logical operators.
If we take the contrapositive of S1, we get:
¬¬Elected ⟹ ¬Corrupt (If a candidate is elected, then he is not known to be corrupt)
Combining the contrapositive of S1 with S2, we get:
If a candidate is elected, then he is not known to be corrupt and is kind.
This statement can be written as:
Elected ⟹ (¬Corrupt ∧ Kind)
So, the correct answer is option C:
If a person is kind, he is not known to be corrupt.
This can be further explained by considering the following cases:
- If a person is corrupt, according to S1, he will not be elected. So, he cannot be kind.
- If a person is kind, according to S2, he will be elected. So, he cannot be known to be corrupt.
Hence, option C is the correct answer.
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Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer?
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Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer?.
Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Consider the following two statements.S1: If a candidate is known to be corrupt, then he will not be electedS2: If a candidate is kind, he will be electedWhich one of the following statements follows from S1 and S2 as per sound inference rules of logic?a)If a person is known to be corrupt, he is kindb)If a person is not known to be corrupt, he is not kindc)If a person is kind, he is not known to be corruptd)If a person is not kind, he is not known to be corruptCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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