Sets and Relations in Math

Question

I have not knowledge about relations, could you help me to solve this excercise step by step, to use in futures excercices?

Thanks for your time.

Given the set $A = \{1, 2, 3, 4\}$ and $B = \{1, 3, 5\}$, and given the relation $R$ in $B$ defined by $$a R b \iff a<b$$ describe the couple relationship and its matrix.

Answer 1

$(a,b)\in R$ if $a<b$ this means, that $(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\in R$

Answer 2

The general way to construct a matrix for a relation between to finite sets $\{a_1,a_2\dots a_m\}$ amd $\{b_1,b_2\dotsb_n\}$ is to create an $m\times n$ matrix X where $x_{i,j}=1$ if $a_i$ is related to $b_i$ and $0$ if they are not related.

In this case the matrix would look like this:

$$ \begin{matrix} 0 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \\ \end{matrix}$$