Relations and Functions
NCERT Class 12
CBSE
Grade 12
Question:
Show that the relation $R$ in the set $A = \{1, 2, 3, 4, 5\}$ given by $R = \{(a, b) : a = b\}$ is an equivalence relation.
Step-by-Step Solution
Reflexive: $a=a \Rightarrow (a,a) \in R$. [1.0 Mark]
Symmetric: $a=b \Rightarrow b=a \Rightarrow (b,a) \in R$. [1.0 Mark]
Transitive: $a=b, b=c \Rightarrow a=c \Rightarrow (a,c) \in R \Rightarrow$ Equivalence relation. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Proving Reflexivity: 1.0 Mark
Proving Symmetry: 1.0 Mark
Proving Transitivity: 1.0 Mark
Correct Answer:
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