Q1: Consider a semigroup with only one element $a$. What is correct?

A1: $a$ is an identity.

A2: $a$ is not a left neutral element.

A3: $a$ is not a right identity.

Q2: Consider the function set $\mathcal{F}([0,1])$ together with the composition. Is $f(x) = \frac{1}{2} x^2$ right-invertible?

A1: No, it’s not because the function is not surjective.

A2: Yes, it is.

A3: No, it’s not because the function is not injective.

Q3: Consider the function set $\mathcal{F}([0,1])$ together with the composition. Is $f(x) = \frac{1}{2} x^2$ left-invertible?

A1: No, it’s not because the function is not surjective.

A2: Yes, it is.

A3: No, it’s not because the function is not injective.