Show that the set s of all positive rationals forms a group under the binary operation .

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5 Properties of Binary Operation 5 Properties of Binary Operation
Prove that the Set of all Positive Rationals with Rational Roots is a Group Prove that the Set of all Positive Rationals with Rational Roots is a Group
Show that the set of all integers forms a group with respect to binary operation def. by a*b=a+b+1 Show that the set of all integers forms a group with respect to binary operation def. by a*b=a+b+1
Show that the set of Q+ forms an abelian group under the operation defined by a * b = ab/2 Show that the set of Q+ forms an abelian group under the operation defined by a * b = ab/2
Show that set of all positive rational numbers forms abelian grp under operation * (a*b = ab /3) Show that set of all positive rational numbers forms abelian grp under operation * (a*b = ab /3)
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
Show that G=R-1 is an abelian group under the binary operation 𝑎∗𝑏=𝑎+𝑏−𝑎𝑏, ∀ 𝑎,𝑏∈𝐺. Show that G=R-1 is an abelian group under the binary operation 𝑎∗𝑏=𝑎+𝑏−𝑎𝑏, ∀ 𝑎,𝑏∈𝐺.
Show that the set of positive rational numbers does not form a group with respect to the binary Show that the set of positive rational numbers does not form a group with respect to the binary