Unable to understand the meaning of $\mathcal{B\pmod t}$

Question

My Question : What is the meaning(/definition) of the image of $\mathcal{B\pmod t}$ ? First of all what is the meaning of $\mathcal{B\pmod t}$ ?

Answer 1

The set $\mathcal{B}\pmod t$ is the set$$\{\text{remainder of the division of $b$ by $t$}\,|\,b\in\mathcal B\}.$$I suppose that its image refers to some function defined before this passage.

Answer 2

Let us suppose that $\mathcal{B}$ is given by $\{1, 4, 8, 11, 15\}$. You are to consider the maps $\mathcal{B} \longrightarrow \mathbb{Z}/t\mathbb{Z}$ for various $t$, and their images. For instance, looking mod $2$, there are elements that are both $0$ and $1$ mod $2$. Looking mod $5$ however, the image is $\{0, 1, 3, 4\}$, as there are no elements that are $2 \bmod 5$ (but there are for the other residue classes).