A binary operation * on the set {0,1,2,3,4,5} is defined as

a*b ={a+b if a+b<6 & a+b-6 if a+b>=6

Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.

 

2 * 3 = 2 + 3 = 5, since 2 + 3 = 5 < 6

4 * 5 = 4 + 5 – 6 = 9 – 6 = 3, since 4 + 5 = 9 ≥ 6

a * (6 – a) = a + (6 – a) – 6 = 0, since a + (6 – a) = 6 ≥ 6

∴ 6 – a is the inverse of a for each a is {0, 1, 2, 3, 4, 5}.

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