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Consider the following statements:
S1: The relation ≤ is reflexive on any set of real numbers.
S2: If R1 and R2 are reflexive relations, R1∪R2 is also reflexive.
S3: Every superset of a symmetric relation is symmetric.
S4: Smallest relation which is irreflexive contains 1 element.
Which of the above statements are false?
  • a)
     Both S3 and S4
  • b)
     Both S1 and S2
  • c)
     Both S1 and S3
  • d)
     Both S2 and S4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the following statements:S1: The relation ≤ is reflexive o...
Defined by xRy if and only if x < y="" is="" a="" partial="" />
S2: The relation defined by xRy if and only if x + y = 10 is an equivalence relation.
Which of the following options is correct?
A) Both S1 and S2 are true.
B) S1 is true but S2 is false.
C) S1 is false but S2 is true.
D) Both S1 and S2 are false.
Free Test
Community Answer
Consider the following statements:S1: The relation ≤ is reflexive o...
As we know,
The statement S1 is true because ∀i,(i ≤ i).
The statement S2 is true because R1∪R2 will contain each element (i,i) which is present in R1 and R2.
The statement S3 is false because there can be some pair which is present in a relation R whose symmetric pair is not present in its superset.
The statement S4 is false because the smallest relation which is irreflexive contains 0 element. A null set is the smallest relation which is irreflexive.
Therefore, both S3 and S4 are false.
Hence, the correct option is (A).
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Consider the following statements:S1: The relation ≤ is reflexive on any set of real numbers.S2: If R1 and R2 are reflexive relations, R1∪R2 is also reflexive.S3: Every superset of a symmetric relation is symmetric.S4: Smallest relation which is irreflexive contains 1 element.Which of the above statements are false?a)Both S3 and S4b)Both S1 and S2c)Both S1 and S3d)Both S2 and S4Correct answer is option 'A'. Can you explain this answer?
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Consider the following statements:S1: The relation ≤ is reflexive on any set of real numbers.S2: If R1 and R2 are reflexive relations, R1∪R2 is also reflexive.S3: Every superset of a symmetric relation is symmetric.S4: Smallest relation which is irreflexive contains 1 element.Which of the above statements are false?a)Both S3 and S4b)Both S1 and S2c)Both S1 and S3d)Both S2 and S4Correct 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 statements:S1: The relation ≤ is reflexive on any set of real numbers.S2: If R1 and R2 are reflexive relations, R1∪R2 is also reflexive.S3: Every superset of a symmetric relation is symmetric.S4: Smallest relation which is irreflexive contains 1 element.Which of the above statements are false?a)Both S3 and S4b)Both S1 and S2c)Both S1 and S3d)Both S2 and S4Correct 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 statements:S1: The relation ≤ is reflexive on any set of real numbers.S2: If R1 and R2 are reflexive relations, R1∪R2 is also reflexive.S3: Every superset of a symmetric relation is symmetric.S4: Smallest relation which is irreflexive contains 1 element.Which of the above statements are false?a)Both S3 and S4b)Both S1 and S2c)Both S1 and S3d)Both S2 and S4Correct answer is option 'A'. Can you explain this answer?.
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