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The binary relation S =  Φ (empty set) on set A = {1, 2,3}  is

  • a)
    neither reflexive nor symmetric

  • b)
    symmetric and relexive

  • c)
    transitive and reflexive

  • d)
    transitive and symmetric

Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The binary relation S = Φ (empty set) on set A = {1, 2,3} isa)neit...
Option D is correct.



  • 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.



Set A is Irreflexive, Symmetric, Anti Symmetric, Asymmetric, Transitive.

But it is not Reflexive.


Thus, option (D) is correct.
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The binary relation S = Φ (empty set) on set A = {1, 2,3} isa)neither reflexive nor symmetricb)symmetric and relexivec)transitive and reflexived)transitive and symmetricCorrect answer is option 'D'. Can you explain this answer?
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