Fsc Part 1 Mathematics (Complete Solution)

Q9
Complete the following table to obtain a semi-group under *

* a b c
a c a b
b a b c
c - - a

SOLUTION:

By associative law

(a*a)*a=a*(a*a)

=> c*a=a*c

=b

Now again associative law

(a*a)*b=a*(a*b)

=>c*b=a*a

    =c 

* a b c
a c a b
b a b c
c c a

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