Question #28

Practice Question

Concept Applied

Cartesian product $A \times B \times A$ consists of ordered triples $(x, y, z)$ where $x \in A$, $y \in B$, $z \in A$. $|A| = 2$, $|B| = 2$. Total ele...

Read Full Step-by-Step Solution →

Question #29

Practice Question

A.{4,5}
B.{1,3,4,5}
C.{2,4,5}
D.{1,3}

Concept Applied

$A \cup B = \{1,2,3\}$, so complement in $U$ is $\{4,5\}$....

Read Full Step-by-Step Solution →

Question #30

Practice Question

A.$A' \cup B'$
B.$A' \cap B'$
C.$A \cap B$
D.$A' \cup B$

Concept Applied

De Morgan's law states $(A \cup B)' = A' \cap B'$....

Read Full Step-by-Step Solution →

Question #31

Practice Question

A.$n(A)+n(B)+n(C)$
B.$n(A)+n(B)+n(C)-n(A\cap B\cap C)$
C.$\sum n - \sum n(\cap pairs) + n(\cap all)$
D.$n(A)+n(B)-n(A\cap C)$

Concept Applied

Inclusion-exclusion principle for three sets....

Read Full Step-by-Step Solution →

Question #32

Practice Question

A.(1, a)
B.{1, a}
C.[1, a]
D.1a

Concept Applied

The Cartesian product $ A \times B $ consists of all ordered pairs where the first element is from A and the second from B. So valid elements are (1,a...

Read Full Step-by-Step Solution →

Question #33

Practice Question

A.(A' \cap B')
B.(A' \cup B')
C.(A \cap B)
D.(A \cup B)

Concept Applied

By De Morgan's law, the complement of a union equals the intersection of the complements: $(A\cup B)' = A'\cap B'$....

Read Full Step-by-Step Solution →

Question #34

Practice Question

A.$B = C$
B.$B \subseteq C$
C.$C \subseteq B$
D.$B \cap C = \emptyset$

Concept Applied

Given $A \cup B = A \cup C$ and $A \cap B = A \cap C$, we use set algebra to deduce $B = C$. Consider elements in $B$ not in $A$: they must appear in ...

Read Full Step-by-Step Solution →

Question #35

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Sets in Class 11. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #36

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Sets....

Read Full Step-by-Step Solution →

Question #37

Practice Question

A.\{1,2,3\}
B.\{4\}
C.\{1,2,3,4\}
D.\{5\}

Concept Applied

$A \cup B = \{1,2,3,4,5,6\}$, $C^c = \{1,2,3,6\}$, intersection is $\{1,2,3,6\} \cap \{1,2,3,6\}$...

Read Full Step-by-Step Solution →

Question #38

Practice Question

Concept Applied

Use $n(M \cup S) = 60 - 10 = 50$, then $n(M \cap S) = 35 + 28 - 50 = 13$....

Read Full Step-by-Step Solution →

Question #39

Practice Question

Concept Applied

Number of subsets =

...

Read Full Step-by-Step Solution →

Question #40

Practice Question

Concept Applied

Cartesian product $A \times B \times A$ consists of ordered triples $(x, y, z)$ where $x \in A$, $y \in B$, $z \in A$. $|A| = 2$, $|B| = 2$. Total ele...

Read Full Step-by-Step Solution →

Question #41

Practice Question

A.{4,5}
B.{1,3,4,5}
C.{2,4,5}
D.{1,3}

Concept Applied

$A \cup B = \{1,2,3\}$, so complement in $U$ is $\{4,5\}$....

Read Full Step-by-Step Solution →

Question #42

Practice Question

A.$A' \cup B'$
B.$A' \cap B'$
C.$A \cap B$
D.$A' \cup B$

Concept Applied

De Morgan's law states $(A \cup B)' = A' \cap B'$....

Read Full Step-by-Step Solution →

Question #43

Practice Question

A.$n(A)+n(B)+n(C)$
B.$n(A)+n(B)+n(C)-n(A\cap B\cap C)$
C.$\sum n - \sum n(\cap pairs) + n(\cap all)$
D.$n(A)+n(B)-n(A\cap C)$

Concept Applied

Inclusion-exclusion principle for three sets....

Read Full Step-by-Step Solution →

Question #44

Practice Question

A.(1, a)
B.{1, a}
C.[1, a]
D.1a

Concept Applied

The Cartesian product $ A \times B $ consists of all ordered pairs where the first element is from A and the second from B. So valid elements are (1,a...

Read Full Step-by-Step Solution →

Question #45

Practice Question

A.(A' \cap B')
B.(A' \cup B')
C.(A \cap B)
D.(A \cup B)

Concept Applied

By De Morgan's law, the complement of a union equals the intersection of the complements: $(A\cup B)' = A'\cap B'$....

Read Full Step-by-Step Solution →

Question #46

Practice Question

A.$B = C$
B.$B \subseteq C$
C.$C \subseteq B$
D.$B \cap C = \emptyset$

Concept Applied

Given $A \cup B = A \cup C$ and $A \cap B = A \cap C$, we use set algebra to deduce $B = C$. Consider elements in $B$ not in $A$: they must appear in ...

Read Full Step-by-Step Solution →

Question #47

Practice Question

A.Theoretical foundations
B.Practical applications
C.Experimental data
D.Historical context

Concept Applied

Foundational check for Sets in Class 11. Study the core principles carefully for competitive exams....

Read Full Step-by-Step Solution →

Question #48

Practice Question

A.A fundamental principle of Mathematics.
B.A complex derivation in JEEMains syllabus.
C.An experimental observation.
D.A theoretical assumption.

Concept Applied

This is a placeholder question to ensure comprehensive syllabus coverage. The correct answer highlights the fundamental nature of Sets....

Read Full Step-by-Step Solution →

Question #49

Practice Question

A.\{1,2,3\}
B.\{4\}
C.\{1,2,3,4\}
D.\{5\}

Concept Applied

$A \cup B = \{1,2,3,4,5,6\}$, $C^c = \{1,2,3,6\}$, intersection is $\{1,2,3,6\} \cap \{1,2,3,6\}$...

Read Full Step-by-Step Solution →

Question #50

Practice Question

Concept Applied

Use $n(M \cup S) = 60 - 10 = 50$, then $n(M \cap S) = 35 + 28 - 50 = 13$....

Read Full Step-by-Step Solution →