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 - Maths - Relations and Functions

Question

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'

Lalit Mehra · Accepted Answer

$a * b = {\begin{matrix} a + b, if a + b < 6 \\ a + b - 6, if a + b \geq 6 \end{matrix}$ 2 * 3 = 2 + 3 = 5, since 2 + 3 = 5 < 6 4 * 5 = 4 + 5 â€“ 6 = 9 â€“ 6 = 3, since 4 + 5 = 9 â‰¥ 6

a * (6 â€“ a) = a + (6 â€“ a) â€“ 6 = 0, since a + (6 â€“ a) = 6 â‰¥ 6 âˆ´ 6 â€“ a is the inverse of a for each a is {0, 1, 2, 3, 4, 5}

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'.

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'.