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Finite and Infinite Sets — IISER Maths MCQs with Solutions
Free IISER Maths Finite and Infinite Sets MCQs with step-by-step solutions (4 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Finite and Infinite Sets · medium · theory
A set is called finite if:
A. it is a subset of $\mathbb{N}$
B. it is empty or its elements can be counted, the counting ending after a definite number ✓ Correct
C. it has at least one element
D. it contains only integers
Solution: A finite set is empty or has a definite number $n$ of elements after which counting stops.
Q2 — Finite and Infinite Sets · hard · theory
The set of rational numbers $\mathbb{Q}$ is:
A. finite
B. empty
C. uncountable
D. infinite (countably infinite) ✓ Correct
Solution: $\mathbb{Q}$ is infinite; moreover it is countably infinite (can be put in one-to-one correspondence with $\mathbb{N}$).
Q3 — Finite and Infinite Sets · hard · theory
Which of the following sets is finite?
A. $\{x \in \mathbb{Q} : 0 < x < 1\}$
B. $\{x \in \mathbb{Z} : x > 5\}$
C. $\{x \in \mathbb{R} : \sin x = 0\}$
D. $\{x \in \mathbb{N} : x^2 - 7x + 12 = 0\}$ ✓ Correct
Solution: $x^2-7x+12=0 \Rightarrow x=3,4$ — a finite (two-element) set; the others are infinite.
Q4 — Finite and Infinite Sets · hard · theory
If $A$ is finite with $n$ elements and $B$ is infinite, then $A \cup B$ is:
A. empty
B. infinite ✓ Correct
C. finite
D. of exactly $n$ elements
Solution: A union containing an infinite set is infinite.