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Relations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations2 Marks
Question
Let A = (3, 5) and B = (7, 11). Let $\text{R}=\{(\text{a, b}):\text{a}\in\text{A},\text{b}\in\text{B, a}-\text{b is odd}\}.$ Show that R is an empty relation from A into B.
✓

Answer

We have,
$\text{A} = \{3, 5\}, \text{ B} = \{7, 11\}$
and $\text{R}=\{(\text{a, b}):\text{a}\in\text{A},\text{b}\in\text{B, a}-\text{b is odd}\}$
For the elements of the given sets A and B, we find that
3 - 7 = -4, 3 - 11 = -8, 5 - 7 = -2 and 5 - 11 = -6
$\therefore\ (3,7)\notin\text{R},( 3,11)\not\in\text{R},(5,7)\not\in\text{R and }(5,11)\notin\text{R}$
Thus, R is an empty relation from A into B.

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