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The binary relation S = ф (empty set) on set A = {1, 2, 3} is :
  • a)
    Neither reflexive nor symmetric
  • b)
    Symmetric and reflexive
  • c)
    Transitive and reflexive
  • d)
    Transitive and symmetric
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The binary relation S = ф (empty set) on set A = {1, 2, 3} is :a...
  • Reflexive : A relation is reflexive if every element of set is paired with itself. Here none of the element of A is paired with themselves, so S is not reflexive.
  • Symmetric : This property says that if there is a pair (a, b) in S, then there must be a pair (b, a) in S. Since there is no pair here in S, this is trivially true, so S is symmetric.
  • Transitive : This says that if there are pairs (a, b) and (b, c) in S, then there must be pair (a,c) in S. Again, this condition is trivially true, so S is transitive. Thus, option (D) is correct. Please comment below if you find anything wrong in the above post.
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The binary relation S = ф (empty set) on set A = {1, 2, 3} is :a)Neither reflexive nor symmetricb)Symmetric and reflexivec)Transitive and reflexived)Transitive and symmetricCorrect answer is option 'D'. Can you explain this answer?
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