Let - - - and - - - Which of the following sets are relations from - to -i - - - - -ii - - - -iii - - - - - - - - -

(i) We note that, R_1⊆ A × B. Thus R_1 is a relation from A to B. (ii) Here, (4, 12)∈ R_2, but (4, 12)∉ A × B. So, R_2 is not a relation from A to B. (iii) He ...

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Byju's Answer

Standard XII

Mathematics

Reflexive Relations

Let 𝐀 = 𝟑,�...

Question

Let 𝐀 = {𝟑,𝟒,𝟕,𝟖} and 𝐁 = {𝟏,𝟕,𝟏𝟎}. Which of the following sets are relations from 𝐀 to 𝐁?
(i) 𝐑𝟏 ={(𝟑,𝟕), (𝟒,𝟕), (𝟕,𝟏𝟎), (𝟖,𝟏)}
(ii) 𝐑𝟐 = {(𝟑,𝟏), (𝟒,𝟏𝟐)}
(iii) 𝐑𝟑 = {(𝟑,𝟕), (𝟒,𝟏𝟎), (𝟕,𝟕), (𝟕,𝟖), (𝟖,𝟏𝟏), (𝟖,𝟕), (𝟖,𝟏𝟎)}.

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Solution

(i) We note that, $R_{1} \subseteq A \times B .$
Thus $R_{1}$ is a relation from A to B.

(ii) Here, $(4, 12) \in R_{2},$ but $(4, 12) \notin A \times B .$
So, $R_{2}$ is not a relation from A to B.

(iii) Here, $(7, 8) \in R_{3},$ but $(7, 8) \notin A \times B .$
So, $R_{3}$ is not a relation from A to B.

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Similar questions

Q. 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)}

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(i) We note that, R1⊆A×B. Thus R1 is a relation from A to B. (ii) Here, (4,12)∈R2, but (4,12)∉A×B. So, R2 is not a relation from A to B. (iii) Here, (7,8)∈R3, but (7,8)∉A×B. So, R3 is not a relation from A to B.