consider our axioms g1g2G3 for a group Of the six possible o

a blnary operation on S (ii) Show that (S, ) is a group. 9. Consider our axioms G1, G2 and G3 for a group. We gave them in the order G1 G2 G3. Conceivable other orders to state the axioms are G1 G3 G2, G2 G1 G3, G2 G3 G1, G3 G1 G2, and G3 G2 G1. Of these six possible orders, exactly three are acceptable for a definition. Which orders are not acceptable, and why? Theory

Solution

If we consider our axioms G1,G2,G3 for a group

And the six possible orders is:G1G2G3,G1G3G2,G2G1G3,G2G3G1,G3G1G2,G3G2G1

If only 3 are acceptable for definition .

here group construction is importent ,

         if we cnstruct group it take factor as position of group.

                   then it acceptable 3 groups only those are:G1G2G3,G2G3G1,G3G1G2.

             In this not even any one group also stay in it\'s same position.

all other 3 are not like this.