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Relations and Functions
NCERT Class 12
CBSE
Grade 12

Question:

If $R = \{(a, b) : a, b \in \mathbb{Z}, a - b \text{ is an integer}\}$, then $R$ is:
(a) An equivalence relation
(b) Reflexive and symmetric but not transitive
(c) Reflexive only
(d) Symmetric only

Step-by-Step Solution

$a-a=0 \in \mathbb{Z}$, $b-a \in \mathbb{Z}$, $a-c \in \mathbb{Z} \Rightarrow$ Equivalence relation. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Selecting Equivalence relation: 1.0 Mark

Correct Answer: An equivalence relation
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