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Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as a * b = {   ???? + ????        ???????? ???? + ???? < ???? ???? + ???? − ????      ???????? ???? + ???? ≥ ???? . Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 – a being the inverse of a.
Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as a * b = {   ???? + ????        ???????? ???? + ???? < ???? ???? + ???? − ????      ???????? ???? + ???? ≥ ???? . Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 – a being the inverse of a.
CBSE | Class 12 | Maths | Miscellaneous | NCERT | Relations and Functions
Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as a * b = {   ???? + ????        ???????? ???? + ???? < ???? ???? + ???? − ????      ???????? ???? + ???? ≥ ???? . Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 – a being the inverse of a.

Arrangement:

Let x = {0, 1, 2, 3, 4, 5} and activity * is characterized as

a * b = { ???? + ???? ???????? ???? + ???? < 6

???? + ???? − 6 ???????? ???? + ???? ≥ 0

Let us say, is the personality for the activity , if ae = a = e*a

That is a = – b or b = 6 – a, which shows a ≠ – b Since x = {0, 1, 2, 3, 4, 5} and

Backwards of a component a ∈ x, a ≠ 0, and a-1 = 6 – a.

i

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