Binary Operation Class 12 #shorts

Binary Operations

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 is chosen at random from the set of all binary operations on a set A containing n elements.The probability that the binary operation is commutative,is

Examine whether the operation '**' defined on R by a**b=ab+1 is : (i) a binary or not (ii) if a binary operation, is it associative or not?

Show that the number of binary operations on {1,2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

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

Write the total number of binary operations on a set consisting of two elements.