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March 14, 2024UGC NET CS 2016 July- paper-2
March 14, 2024UGC NET CS 2016 July- paper-2
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Question 3
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Suppose that R 1 and R 2 are reflexive relations on a set A.
Which of the following statements is correct ?
Which of the following statements is correct ?
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R 1 ∩ R 2 is reflexive and R 1 ∪ R 2 is irreflexive.
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R 1 ∩ R 2 is irreflexive and R 1 ∪ R 2 is reflexive.
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Both R 1 ∩ R 2 and R 1 ∪ R 2 are reflexive.
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Both R 1 ∩ R 2 and R 1 ∪ R 2 are irreflexive.
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Question 3 Explanation:
A binary relation R over a set X is reflexive if every element of X is related to itself. Formally, this may be written ∀ x ∈X : xRx.
Ex: Let set A={0,1}
R 1 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 2 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 1 ∩ R 2 must have {(0,0),(1,1)} is reflexive.
R 1 ∪ R 2 must have {(0,0),(1,1)} is reflexive.
Ex: Let set A={0,1}
R 1 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 2 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 1 ∩ R 2 must have {(0,0),(1,1)} is reflexive.
R 1 ∪ R 2 must have {(0,0),(1,1)} is reflexive.
Correct Answer: C
Question 3 Explanation:
A binary relation R over a set X is reflexive if every element of X is related to itself. Formally, this may be written ∀ x ∈X : xRx.
Ex: Let set A={0,1}
R 1 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 2 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 1 ∩ R 2 must have {(0,0),(1,1)} is reflexive.
R 1 ∪ R 2 must have {(0,0),(1,1)} is reflexive.
Ex: Let set A={0,1}
R 1 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 2 ={(0,0),(1,1)} all diagonal elements we are considering for reflexive relation.
R 1 ∩ R 2 must have {(0,0),(1,1)} is reflexive.
R 1 ∪ R 2 must have {(0,0),(1,1)} is reflexive.
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