if the number of different reflexive relation on set A is equal to no. of different symmetric relation on set A then n(A) is ?/

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Please find below the solution to the asked query:

We know that if a set A has 'n' elements, then:Number of reflexive relation=2n2-nNumber of symmetric relation=2nn+12Acoording to question:Number of reflexive relation=Number of symmetric relation2n2-n=2nn+12n2-n=nn+122n2-2n=n2+n2n2-n2-2n-n=0n2-3n=0nn-3=0Assuming that set is non empty so n0n=3 Answer


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