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Consider the binary operation ^^ on the...

Consider the binary operation `^^` on the set `{1,2,3,4,5}` given by the following multiplication table.
(i) Compute (2*3)*4 and 2*(3*4)
(ii) Is * commutative ?
(iii) Compute (2*3) *(4*5)
(Hint : uset the following table )

Text Solution

Verified by Experts

(i) `(**3)**4=1**4=1`
and `2**(3**4)=2**1=1`
(ii) `:. ` For each `a,bin {1,2,3,4,5)`
`a**b=b**a`
`:. **` is commutative .
(iii) `(2**3)**(4**5)=1**1=1`
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