Binary Operation on Sets

Binary Operations

If * is a binary operation on set Q of rational numbers defined as a ^(*)b=(ab)/(5) Write the identity for ^(*), if any

Let * be a binary operation on set of integers I, defined by a*b=2a+b-3. Find the value of 3*4.

Let * be a binary operation on set of integers I, defined by a ^(*)b=2a+b-3. Find the value of 3^(*)4

Let ^(*) be a binary operation on set Q-[1] defined by a*b=a+b-ab for all a,b in Q-[1]. Find the identity element with respect to * on Q. Also,prove that every element of Q-[1] is invertible.

Let A be a non-empty set and S be the set of all functions from A to itself. Prove that the composition of functions 'o' is a non-commutative binary operation on Sdot Also, prove that 'o' is an associative binary operation on Sdot

Define a binary operation on a set.

Define a commutative binary operation on a set.

Define an associative binary operation on a set.

A binary operation on a set has always the identity element.