Question

Let 𝐀 = {𝟏,𝟐,𝟑,𝟕} and 𝐁 = {𝟑,𝟎,–𝟏,𝟕}, which of the following are relation from 𝐀 to 𝐁?
(i) 𝐑𝟏 = {(𝟐,𝟏), (𝟕,𝟏)}
(ii) 𝐑𝟐 = {(–𝟏,𝟏)}
(iii) 𝐑𝟑 = {(𝟐,–𝟏), (𝟕,𝟕), (𝟏,𝟑)}
(iv) 𝐑𝟒 = {(𝟕,–𝟏), (𝟎,𝟑), (𝟑,𝟑), (𝟎,𝟕)}

Answer 1

(i) Here, $(2,1),(7,1)\in R_1,$ but $(2,1),(7,1)\notin A\times B.$
Thus $R_1$ is not a relation from A to B.

(ii) Here, $(-1,1)\in R_2,$ but $(-1,1)\notin A\times B.$
So, $R_2$ is not a relation from A to B.

(iii) We note that, $R_3\subseteq A\times B.$
So, $R_3$ is a relation from A to B.

(iv) Here, $(0,3),(0,7)\in R_4,$ but $(0,3),(0,7)\notin A\times B$
So, $R_4$ is not a relation from A to B.