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Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:
S1: There is a subset of S that is larger than every other subset.
S2: There is a subset of S that is smaller than every other subset.
S2: There is a subset of S that is smaller than every other subset.
Q. Which one of the following is CORRECT?
- a)Both S1 and S2 are true
- b)S1 is true and S2 is false
- c)S2 is true and S1 is false
- d)Neither S1 nor S2 is true
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following relation on subsets of the set S of integers be...
According to the given information :
S1 is true because NULL set is smaller than every other set.
S2 is true because the UNIVERSAL set {1, 2, ..., 2014} is larger than every other set.
Thus, both S1 and S2 are true.
Please comment below if you find anything wrong in the above post.
S1 is true because NULL set is smaller than every other set.
S2 is true because the UNIVERSAL set {1, 2, ..., 2014} is larger than every other set.
Thus, both S1 and S2 are true.
Please comment below if you find anything wrong in the above post.
Most Upvoted Answer
Consider the following relation on subsets of the set S of integers be...
Given:
- Relation on subsets of the set S of integers between 1 and 2014.
- U V if the minimum element in the symmetric difference of the two sets is in U.
- S1: There is a subset of S that is larger than every other subset.
- S2: There is a subset of S that is smaller than every other subset.
To prove:
- Both S1 and S2 are true.
Explanation:
1. S1: There is a subset of S that is larger than every other subset.
Let's consider the power set of S, denoted as P(S), which contains all possible subsets of S. The size of P(S) is 2^2014, which is a finite number.
- Proof by contradiction:
Assume that there is no subset in S that is larger than every other subset. This means that for every subset U in S, there exists a subset V in S such that V is larger than U.
- Constructing a contradiction:
Consider the set S' that contains every element of S except for the minimum element. Since S' is a subset of S, it must also satisfy the relation U V. However, there is no subset in S that is larger than S' (as S' is missing the minimum element), which contradicts our assumption.
- Conclusion:
Hence, our assumption is false, and there must exist a subset of S that is larger than every other subset.
2. S2: There is a subset of S that is smaller than every other subset.
Let's consider the empty set, denoted as Ø. The empty set is a subset of every other set, including itself.
- Proof:
For any subset U in S, the symmetric difference between U and Ø is U itself, as Ø does not contain any elements. Therefore, the minimum element in the symmetric difference is in U, satisfying the relation U Ø.
Conclusion:
- Both S1 and S2 are true, as we have proved the existence of a subset of S that is larger than every other subset (S1) and a subset of S that is smaller than every other subset (S2). Hence, the correct answer is option A.
- Relation on subsets of the set S of integers between 1 and 2014.
- U V if the minimum element in the symmetric difference of the two sets is in U.
- S1: There is a subset of S that is larger than every other subset.
- S2: There is a subset of S that is smaller than every other subset.
To prove:
- Both S1 and S2 are true.
Explanation:
1. S1: There is a subset of S that is larger than every other subset.
Let's consider the power set of S, denoted as P(S), which contains all possible subsets of S. The size of P(S) is 2^2014, which is a finite number.
- Proof by contradiction:
Assume that there is no subset in S that is larger than every other subset. This means that for every subset U in S, there exists a subset V in S such that V is larger than U.
- Constructing a contradiction:
Consider the set S' that contains every element of S except for the minimum element. Since S' is a subset of S, it must also satisfy the relation U V. However, there is no subset in S that is larger than S' (as S' is missing the minimum element), which contradicts our assumption.
- Conclusion:
Hence, our assumption is false, and there must exist a subset of S that is larger than every other subset.
2. S2: There is a subset of S that is smaller than every other subset.
Let's consider the empty set, denoted as Ø. The empty set is a subset of every other set, including itself.
- Proof:
For any subset U in S, the symmetric difference between U and Ø is U itself, as Ø does not contain any elements. Therefore, the minimum element in the symmetric difference is in U, satisfying the relation U Ø.
Conclusion:
- Both S1 and S2 are true, as we have proved the existence of a subset of S that is larger than every other subset (S1) and a subset of S that is smaller than every other subset (S2). Hence, the correct answer is option A.
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Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer?
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Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer?.
Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer?.
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Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:S1: There is a subset of S that is larger than every other subset.S2: There is a subset of S that is smaller than every other subset.Q. Which one of the following is CORRECT?a)Both S1 and S2 are trueb)S1 is true and S2 is falsec)S2 is true and S1 is falsed)Neither S1 nor S2 is trueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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