(a) Show that the set $Q^+$ of all positive rational numbers form an…

Question

(a) Show that the set $Q^+$ of all positive rational numbers form an abelian group under operation $o$ defined by : $aob = \frac{ab}{2}, \forall a,b \in Q^+$.

(b) Show that the intersection of two subgroups of a group is again a subgroup.

(c) Show that the sum of first '$n$' natural numbers is $\frac{n(n+1)}{2}$.

Related pages

• Principle of Mathematical Induction — topic
• Discrete Mathematics syllabus

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