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Elementary Group Theory

Show that the set of all positive rational numbers forms an abelian group under the composition a*b=ab/4.

Show that the set S= {-1,0,1} does not form a group with respect to addition operation

Let G= {0,1,2} form a composition table for G under addition modulo 3. Find the identity element and inverse element of 1 and 2.

Test the closure, associative and commutative properties for the operation defined by m*n=m+n+1 ,m,n ϵ Z.

S is a given set and a,b ϵ S. Prove that the operation * defined by a*b= 3a+5b on S=set of positive integers, is a binary operation.

Class Twelve

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