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anonymous

  • one year ago

a relation R is defined in NxN such that (a,b)R(c,d) if a+d=b+c .prove that relation R is equivalence relation.

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  1. mathmate
    • one year ago
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    A binary relation is an equivalence relation iff it satisfies the following properties: 1. reflexivity 2. symmetry 3. transistivity. using the condition a+d=b+c, are you able to show that the given relation satisfies all of the above properties? @heena94637

  2. anonymous
    • one year ago
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    I know about these properties but I am confused how to prove these properties in this equation .please explain if u can.

  3. mathmate
    • one year ago
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    Hints: Given (a,b)R(c,d) where a+d=b+c. 1. Reflexivity : operating on itself you need to show (a,b)R(a,b) satisfies the relation: |dw:1439721405073:dw| substitute a=a, b=b, c=a, d=b into a+d=b+c to get a+b=b+a which is true. Therefore reflexivity is satisfied. 2. Symmetry : switching the first and second operands show that (c,d)R(a,b) is a relation R. 3. Transistivity: show that if (a,b)R(c,d), (c,d)R(e,f) are both relations, then (a,b)R(e,f) is also a relation.

  4. anonymous
    • one year ago
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    thanks mathmate

  5. mathmate
    • one year ago
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    You're welcome! :)

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