Binary Operation

The identity element for the binary operation $*$ defined by $a^{*} b=\frac{ab}{2}, a, b\in Q_0$ (the set of all non-zero rational numbers) is

If any one of the columns of the composition table for a binary operation $*$ on a set $S$ coincides with the left most column of the table, then

If $N$ is a set of natural numbers, then under binary operation $a·b=a+b,( N,·)$ is

Let $a$ be any element in a boolean algebra $B.$ If $a+x=1$ and $ax=0,$ then

If any one of the rows of the composition table for a binary operation$*$ on a set $S$ coincides with the top most row of the table, then

The composition table for a binary operation, $*$ defined on a set $S$ is symmetric about the leading diagonal, then