Let S be the set of all rational numbers except 1 and * be defined on S by `a*b=a+b-a b ,` for a...

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Let Q-1 be the set of all rational numbers except -1 and o be a binary operation defined by aob=a+b+ Let Q-1 be the set of all rational numbers except -1 and o be a binary operation defined by aob=a+b+
Let S be the set of all rational numbers of the form m/n, where m∈Z and n = 1,2,3. Prove that * on S Let S be the set of all rational numbers of the form m/n, where m∈Z and n = 1,2,3. Prove that * on S
Find the identity element in the set of all rational except -1 with respect to *defined a*b= a+b+ab Find the identity element in the set of all rational except -1 with respect to *defined a*b= a+b+ab
On Q, the set of all rational numbers, * is defined by a∗b = (a-b)/2 show that * is not associative. On Q, the set of all rational numbers, * is defined by a∗b = (a-b)/2 show that * is not associative.
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Show that the set Q1 of all rational number other than 1 with the operation defined a*b = a+b-ab is Show that the set Q1 of all rational number other than 1 with the operation defined a*b = a+b-ab is
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Show that set of rational numbers not equal to -1 is an abelian group under a.b = a + b + ab Show that set of rational numbers not equal to -1 is an abelian group under a.b = a + b + ab