UGC NET CS 2008 Dec-Paper-2
January 20, 2024Question 3971 – 2006 December UGC NET Paper 1
January 20, 2024UGC NET CS 2008 Dec-Paper-2
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Question 12
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A relation R in {1, 2, 3, 4, 5, 6} is given by { (1, 2), (2, 3), (3, 4), (4, 4), (4, 5) }. This relation is :
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reflexive
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symmetric
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transitive
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not reflexive, not symmetric and not transitive
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Question 12 Explanation:
Reflexive: A relation R is said to be reflexive if for all elements of a set x belongs to R (x,x) exists.
Since in above question {(1,1), (2,2),(3,3),(4,4),(5,5),(6,6)} does not exist in given relation so it is not reflexive.
Symmetric: A relation R is symmetric if (x,y) belong to R then (y,x) must belong to R.
Since in above question (1,2) exists but (2,1) does not exist in given relation so given relation is not symmetric.
Transitive: A relation is transitive if (x,y) belongs to R and (y,z) belongs to R then (x,z) must belongs to R.
In above question (1, 2), (2, 3) exist in given relation but (1,3) does not exist there so given relation is not transitive.
Hence correct option is option(D)
Since in above question {(1,1), (2,2),(3,3),(4,4),(5,5),(6,6)} does not exist in given relation so it is not reflexive.
Symmetric: A relation R is symmetric if (x,y) belong to R then (y,x) must belong to R.
Since in above question (1,2) exists but (2,1) does not exist in given relation so given relation is not symmetric.
Transitive: A relation is transitive if (x,y) belongs to R and (y,z) belongs to R then (x,z) must belongs to R.
In above question (1, 2), (2, 3) exist in given relation but (1,3) does not exist there so given relation is not transitive.
Hence correct option is option(D)
Correct Answer: D
Question 12 Explanation:
Reflexive: A relation R is said to be reflexive if for all elements of a set x belongs to R (x,x) exists.
Since in above question {(1,1), (2,2),(3,3),(4,4),(5,5),(6,6)} does not exist in given relation so it is not reflexive.
Symmetric: A relation R is symmetric if (x,y) belong to R then (y,x) must belong to R.
Since in above question (1,2) exists but (2,1) does not exist in given relation so given relation is not symmetric.
Transitive: A relation is transitive if (x,y) belongs to R and (y,z) belongs to R then (x,z) must belongs to R.
In above question (1, 2), (2, 3) exist in given relation but (1,3) does not exist there so given relation is not transitive.
Hence correct option is option(D)
Since in above question {(1,1), (2,2),(3,3),(4,4),(5,5),(6,6)} does not exist in given relation so it is not reflexive.
Symmetric: A relation R is symmetric if (x,y) belong to R then (y,x) must belong to R.
Since in above question (1,2) exists but (2,1) does not exist in given relation so given relation is not symmetric.
Transitive: A relation is transitive if (x,y) belongs to R and (y,z) belongs to R then (x,z) must belongs to R.
In above question (1, 2), (2, 3) exist in given relation but (1,3) does not exist there so given relation is not transitive.
Hence correct option is option(D)