QB_PH_GA_024: Analytical & Spatial Aptitude

Which of the following capital English letters remains completely identical to itself under BOTH horizontal reflection (water image) AND vertical reflection (mirror image)?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Reflectional Symmetry Definitions**: - Mirror image: Reflection across a vertical mirror line ($x \to -x$). - Water image: Reflection across a horizontal mirror line ($y \to -y$). 2. **Inspection of Letters**: - **A**: Vertical mirror $\implies$ invariant; Horizontal (water) $\implies$ inverted ($\\forall$). - **E**: Vertical mirror $\implies$ backwards ($\\exists$); Horizontal (water) $\implies$ invariant. - **M**: Vertical mirror $\implies$ invariant; Horizontal (water) $\implies$ W. - **H**: Vertical mirror $\implies$ H; Horizontal (water) $\implies$ H (Both invariant). 3. **Conclusion**: Letter 'H' satisfies both. Option (A) is correct.