Let a relation be defined on a set of functions defined on R→R 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, f−f=0∈R
Symmetric: f - g is even
g - f is even so (g,f)∈R
Transitive ∀(f,g)∈R,(g,h)∈R ⇒f−g is even, g - h is even ⇒f−h is even
So R is equivalence Relation.