Equal Sets — IISER Maths MCQs with Solutions
Free IISER Maths Equal Sets MCQs with step-by-step solutions (5 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Equal Sets · medium · theory
If $A = \{x : x \text{ is a multiple of } 2\}$ and $B = \{x : x \text{ is an even integer}\}$, then:
A. $A = B$ ✓ Correct
B. $A \subset B$ strictly
C. $B \subset A$ strictly
D. $A$ and $B$ are disjoint
Solution: "Multiple of 2" and "even integer" describe exactly the same numbers, so $A=B$.
Q2 — Equal Sets · hard · theory
Sets $A$ and $B$ satisfy $A \subseteq B$ and $B \subseteq A$. Then:
A. $A \subset B$ strictly
B. nothing can be concluded
C. $A$ and $B$ are disjoint
D. $A = B$ ✓ Correct
Solution: Mutual inclusion $A\subseteq B$ and $B\subseteq A$ is precisely the definition of set equality: $A=B$.
Q3 — Equal Sets · hard · theory
If $\{2a + b,\ a - b\} = \{5,\ 1\}$ with $a - b = 1$, then the value of $a$ is:
A. $2$ ✓ Correct
B. $4$
C. $3$
D. $1$
Solution: From the pairing $a-b=1$ and $2a+b=5$: adding, $3a=6 \Rightarrow a=2$ (then $b=1$).
Q4 — Equal Sets · medium · theory
Two finite sets $A$ and $B$ have $n(A) = n(B)$. Then $A$ and $B$ are necessarily:
A. disjoint
B. equal
C. equivalent, but not necessarily equal ✓ Correct
D. subsets of each other
Solution: Same cardinality means equivalent; they need not have the same elements, so not necessarily equal.
Q5 — Equal Sets · medium · theory
The sets $A = \{x \in \mathbb{R} : x^2 = x\}$ and $B = \{0, 1\}$ are:
A. equivalent but not equal
B. equal ✓ Correct
C. such that $A \subset B$ strictly
D. disjoint
Solution: $x^2=x \Rightarrow x(x-1)=0 \Rightarrow x=0,1$, so $A = \{0,1\} = B$.