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Relations & Functions — GSEB Class 12 (HSC)

Master Relations & Functions for GSEB Class 12 (HSC). Free verified step-by-step solutions, 2 past exam problems, formulas, and markschemes.

Exam Questions & Step-by-Step Markschemes (2 Problems)

Question 1 • 2023 3 Marks

          Show that the relation R in the set \mathbb{Z} of integers given by R = \{(a, b) : 2 \text{ divides } (a - b)\} is an equivalence relation.
        

Answer: R \text{ is reflexive, symmetric, and transitive } \implies \text{Equivalence Relation}

Question 2 • 2024 4 Marks

          Prove that: \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{5}\right) + \tan^{-1}\left(\frac{1}{8}\right) = \frac{\pi}{4}
        

Answer: \text{LHS} = \frac{\pi}{4} = \text{RHS} \quad (\text{Proved})

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