Sets, Relations & Functions
Sets and Relations
nta_pyq_2025_jan
Grade 11
Question:
Let S = N \cup {0}. Define a relation R from S to R by : 2 R = {(x, y) : log y = x log ( ), x \in S, y \in R} e e 5 Then, the sum of all the elements in the range of R is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
S = {0, 1, 2, 3 \ldots \ldots} 2 (4) log y y = log ( e ) 5 x 2 \Rightarrow y = ( ) 5 Required 1 2 3 2 2 2 1 5 Sum = 1 + ( ) + ( ) + ( ) + \ldots..- = = 5 5 5 2 3 1- 5
Correct Answer: 4