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Question

Let a relation be defined on a set of functions defined on RR such that R ={(f, g): f-g is an even function} then R is

A
Reflexive but not symmetric
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B
Not reflexive but symmetric & transitive
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C
Symmetric but not transitive
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D
Equivalence relation
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Solution

The correct option is D Equivalence relation
Reflexive, ff=0R
Symmetric: f - g is even
g - f is even so (g,f)R
Transitive (f,g)R,(g,h)R
fg is even, g - h is even
fh is even
So R is equivalence Relation.

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