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Universal Set — JEE Main Mathematics MCQs with Solutions
Free JEE Main Mathematics Universal Set MCQs with step-by-step solutions (11 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Universal Set · easy · theory
The universal set for a particular discussion is:
A. a set that contains all objects under consideration in that context ✓ Correct
B. always an infinite set
C. the empty set
D. always the set of natural numbers
Solution: The universal set $U$ contains all the elements relevant to the particular context being studied.
Q2 — Universal Set · medium · theory
For the study of subsets of integers, the most appropriate universal set is:
A. $\mathbb{Z}$ ✓ Correct
B. $\mathbb{N}$
C. $\mathbb{R}$
D. $\emptyset$
Solution: When all sets under discussion are sets of integers, $\mathbb{Z}$ serves naturally as the universal set.
Q3 — Universal Set · medium · theory
If $U$ is the universal set and $A \subseteq U$, then $A \cup A'$ equals:
A. $A'$
B. $\emptyset$
C. $A$
D. $U$ ✓ Correct
Solution: A set together with its complement fills the universal set: $A \cup A' = U$.
Q4 — Universal Set · medium · theory
If $U$ is the universal set and $A \subseteq U$, then $A \cap A'$ equals:
A. $A$
B. $U$
C. $A'$
D. $\emptyset$ ✓ Correct
Solution: A set and its complement have no common element: $A \cap A' = \emptyset$.
Q5 — Universal Set · medium · theory
The complement of a set $A$ is taken with respect to:
A. the empty set
B. the set $A$ itself
C. the power set of $A$
D. the universal set $U$ ✓ Correct
Solution: $A' = U - A = \{x \in U : x \notin A\}$, defined relative to the universal set.
Q6 — Universal Set · medium · numerical
If $U = \{1, 2, 3, \dots, 10\}$ and $A = \{2, 4, 6, 8, 10\}$, then $A'$ is:
A. $\{1, 2, 3, 4, 5\}$
B. $\{1, 3, 5, 7, 9\}$ ✓ Correct
C. $\{2, 4, 6, 8\}$
D. $\emptyset$
Solution: $A' = U - A = \{1,3,5,7,9\}$ (the odd numbers up to 10).
Q7 — Universal Set · medium · theory
Which set can serve as a universal set for $A = \{1, 3\}$, $B = \{2, 4\}$, and $C = \{3, 5\}$?
A. $\{1, 2, 3\}$
B. $\{1, 3, 5\}$
C. $\{1, 2, 3, 4, 5\}$ ✓ Correct
D. $\{2, 4\}$
Solution: A universal set must contain all elements of $A$, $B$ and $C$: $\{1,2,3,4,5\}$ does.
Q8 — Universal Set · hard · theory
If $U$ is the universal set, then $U'$ (the complement of $U$) is:
A. the power set of $U$
B. $\emptyset$ ✓ Correct
C. $U$
D. undefined
Solution: $U' = U - U = \emptyset$; the universal set has an empty complement.
Q9 — Universal Set · medium · theory
For $A \subseteq U$, the statement $(A')' = A$ expresses that:
A. complementation is not defined
B. a set equals its complement
C. the complement of $U$ is $U$
D. the complement of the complement of a set is the set itself ✓ Correct
Solution: Complementing twice returns the original set: $(A')' = A$.
Q10 — Universal Set · medium · numerical
If $U = \{x \in \mathbb{N} : x \le 20\}$ and $A$ is the set of primes in $U$, then $n(A')$ is:
A. $11$
B. $13$
C. $8$
D. $12$ ✓ Correct
Solution: Primes $\le 20$: 2,3,5,7,11,13,17,19 = 8, so $n(A') = 20 - 8 = 12$.
Q11 — Universal Set · hard · theory
For subsets of a universal set $U$, the statement 'if $A \subseteq B$ then $B' \subseteq A'$' is:
A. true only if $A = B$
B. always false
C. always true ✓ Correct
D. true only if $A = \emptyset$
Solution: Complementation reverses inclusion, so this holds for all subsets $A \subseteq B$.