Define Binary Operation.

Define a binary operation on a set

Define a binary opertion ** on the set {0,1,2,3,4,5} as a**b ={{:(a+b"," , if a + b lt 6), ( a + b -6, if a + b ge 6):} Show that zero is the identity for this operation and each element ane 0 of the set is invertible with 6-a being the inverse of a.

Let * be a Binary operation defined on N by a ** b = 2^(ab) . Prove that * is commutative.

In a group Q-{-1} under binary operation '+' defined by a^("*")b=a+b+ab , then inverse of 10 is :

Consider a binary operation ** on N defined as a **b=a ^(3) +b ^(3). Choose the correct answer.

Verify whether the binary operation * on Q, the set of all rationals, defined as a*b=ab+1 is commutative or associative.

If A={a,b,c} , then the number of binary operations on A is

Define Binary fission, and illustrate binary fission in Amoeba.