<p>Match number of integers in each set with (P)0 (Q)2 (R)3 (S)less than 3 (T)more than 3</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>(A) ln{x}: {x}>0 excludes integers → 0 integers → (P),(S)</p><p>(B) Domain has exactly 3 admissible integers → (R)</p><p>(C) (x-1)²+1 on [0,2]: range [1,2], integers={1,2}: 2 → (Q),(S)</p><p>(D) [x]∈{-5,...,5}: range values √(25-n²) integers when n²=0,9,16,25 → 4+ integers → (T)</p><p><strong>Answer: A→P,S; B→R; C→Q,S; D→T</strong></p><div class="trap-box"><strong>Trap:</strong> Don't count real values — count only integers.</div><div class="key-concept"><strong>Key Concept:</strong> Integer counting in domain/range — direct integer testing is fastest</div></div>
Correct Answer: A→P,S; B→R; C→Q,S; D→T