Let \( Q \) be the set of all rational numbers. Define an operation...

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Let Q be the set of all rational numbers and * be the binary operation , defined by Let Q be the set of all rational numbers and * be the binary operation , defined by
Let the set of rational number except -1,show that Q* forms an infinite abelian group a* b = a+b+ ab Let the set of rational number except -1,show that Q* forms an infinite abelian group a* b = a+b+ ab
On the set Q of all rational numbers an operation * is defined by `a*b = 1 + ab`. Show that * On the set Q of all rational numbers an operation * is defined by `a*b = 1 + ab`. Show that *
Q^+ is the set of all positive rational numbers with the binary operation * defined by a∗b=ab/2 Q^+ is the set of all positive rational numbers with the binary operation * defined by a∗b=ab/2
Q, the set of all rational number, * is defined by `a*b=(a-b)/2` , show that * is no associative. Q, the set of all rational number, * is defined by `a*b=(a-b)/2` , show that * is no associative.
Show that set Q+ of all +ve rational numbers forms an abelian group under operation * (a*b = ab/2) Show that set Q+ of all +ve rational numbers forms an abelian group under operation * (a*b = ab/2)
The set Q of all rational number, operation * is defined by a*b=a+b+ab forms a commutative monoid The set Q of all rational number, operation * is defined by a*b=a+b+ab forms a commutative monoid
Show that the set Q Show that the set Q' of all rational number other than -1 with the operation defined by a*b=a+b+ab