Q10 of 123 Page 3

Define identity element for a binary operation defined on a set.

If A be the non-empty set and * be the binary operation on A. An element e is the identity element of a ∈ A, if a * e = a = e * a.

If the binary operation is addition(+), e = 0 and for * is multiplication(×), e = 1.


More from this chapter

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8

Let * be a binary operation, on the set of all non-zero real numbers, given by for all a, b ∈ R – {0}. Write the value of x given by 2 * (x * 5) = 10.

 9

Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, …, 10}.

 11

Write the composition table for the binary operation multiplication modulo 10(×10) on the set S = {2, 4, 6, 8}.

 12

For the binary operation multiplication modulo 10(×10) defined on the set S = {1, 3, 7, 9}, write the inverse of 3.