Class CBSE Class 12 Mathematics Relations and Functions Q #1407
KNOWLEDGE BASED
REMEMBER
3 Marks 2025 AISSCE(Board Exam) SA
Let $A=\{1,2,3\}$ and $B=\{4,5,6\}$. A relation R from A to B is defined as $R=\{(x,y):x+y=6, x\in A, y\in B\}$. (i) Write all elements of R. (ii) Is R a function? Justify. (iii) Determine domain and range of R.
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Detailed Solution

Step 1: Find elements of R

We are given $A=\{1,2,3\}$ and $B=\{4,5,6\}$. The relation R from A to B is defined as $R=\{(x,y):x+y=6, x\in A, y\in B\}$. We need to find all pairs $(x,y)$ such that $x \in A$, $y \in B$, and $x+y=6$. If $x=1$, then $y=6-1=5$. So, $(1,5) \in R$. If $x=2$, then $y=6-2=4$. So, $(2,4) \in R$. If $x=3$, then $y=6-3=3$. But $3 \notin B$, so $(3,3) \notin R$. Therefore, $R = \{(1,5), (2,4)\}$.

Step 2: Check if R is a function

A relation R from A to B is a function if every element in A has a unique image in B. In other words, for every $x \in A$, there should be exactly one $y \in B$ such that $(x,y) \in R$. Here, $R = \{(1,5), (2,4)\}$. The domain of R is $\{1,2\}$. Since $3 \in A$ but there is no $y \in B$ such that $(3,y) \in R$, R is not a function from A to B.

Step 3: Determine the domain of R

The domain of R is the set of all first elements in the ordered pairs of R. Domain of $R = \{1, 2\}$.

Step 4: Determine the range of R

The range of R is the set of all second elements in the ordered pairs of R. Range of $R = \{4, 5\}$.

Final Answer: R = {(1,5), (2,4)}. R is not a function. Domain of R = {1, 2}. Range of R = {4, 5}.

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Pedagogical Audit
Bloom's Analysis: This is an REMEMBER question because the student needs to recall the definition of a relation, a function, domain, and range to answer the question.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of relations, functions, domain, and range, rather than just recalling facts or performing calculations.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of the definitions and properties of relations and functions, which are core concepts in the syllabus.

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