1.

If the binary operation o is defined by a O b = a + b – ab on the set Q – {-1} of all rational numbers other than 1, show that o is commutative on Q – [1].

Answer»

Let a, b ∈ Q – {-1}.

Now, aob = a + b – ab

= b + a – ba

= boa

So,

aob = boa for all a, b ∈ Q – {-1}

Hence, o is commutative on Q – {-1}


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