CBSE Class 12 Mathematics Relations and Functions Q #2108
KNOWLEDGE BASED
APPLY
2 Marks 2014 Generic-Curriculum VSA
Let $R = \{(a, a^3) : a \text{ is a prime number less than } 5\}$ be a relation. Find the range of $R$.
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Detailed Solution

Step 1: Identify the domain elements

The relation $R$ is defined for $a$, where $a$ is a prime number less than $5$. The prime numbers less than $5$ are $2$ and $3$. Thus, the set of values for $a$ is $\{2, 3\}$.

Step 2: Determine the ordered pairs

For each $a$, the corresponding element in the relation is $a^3$.
If $a = 2$, then $a^3 = 2^3 = 8$. The ordered pair is $(2, 8)$.
If $a = 3$, then $a^3 = 3^3 = 27$. The ordered pair is $(3, 27)$.
Therefore, $R = \{(2, 8), (3, 27)\}$.

Step 3: Identify the range

The range of a relation is the set of all second elements of the ordered pairs. From the set $R$, the second elements are $8$ and $27$.

Final Answer: {8, 27}

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must apply the definition of a relation and the concept of range to a specific set of prime numbers.
Knowledge Dimension: PROCEDURAL
Justification: The student follows a step-by-step algorithm to identify domain elements, compute outputs, and extract the range.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE (Textbook). This question tests the foundational understanding of Relations and Functions (Chapter 1) as per the NCERT curriculum.

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