Question:

<div class="solution"><p>(A) False for infinite sets (e.g. n↦n+1 on ℕ)</p><p>(B) False for infinite sets</p><p>(C) If f(x_1)=f(x_2), then (g∘f)(x_1)=(g∘f)(x_2); injectivity of g∘f forces x_1=x_2. ✓</p><p>(D) Each of 3 elements has 2 choices: 2^3=8 ✓</p><p><strong>Answer: (C),(D)</strong></p><div class="trap-box"><strong>Trap:</strong> (A) and (B) are true only for finite sets. For infinite sets both fail.<div class="key-concept"><strong>Key Concept:</strong> g∘f injective ⟹ f injective (standard composition rule)