BECE Mathematics 2018 Paper

Concept:An infinite set is a set whose elements cannot be counted completely because they continue endlessly.Explanation:A finite set has a countable number of elements, which can be listed completely.Option A: $\{1,2,\dots,5,6,7\}$ contains only the numbers from $1$ to $7$, so it is finite.Option B: $\{4,6,8,10,12\}$ has exactly five elements, so it is finite.Option D: $\{3,6,\dots,18,21,\dots,33,36\}$ lists multiples of $3$ up to $36$, so its elements can be fully counted; it is finite.Option C: $\{2,3,5,7,11,\dots\}$ lists prime numbers and the trailing “$\dots$” shows the list continues forever.Since prime numbers never end, this set has infinitely many elements.Answer:The infinite set is option C: $\{2,3,5,7,11,\dots\}$.