(B) By the definition of set difference,the set $A - B$ consists of all elements that are in $A$ but not in $B$.This is equivalent to the intersection

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(B) By the definition of set difference,the set $A - B$ consists of all elements that are in $A$ but not in $B$.This is equivalent to the intersection of $A$ and the complement of $B$.Therefore,$A - B = A \cap \bar{B}$.

Class 11 Mathematics Set Theory Complement of a Set

Medium

If $A = \{x : x \text{ is a multiple of } 3\}$ and $B = \{x : x \text{ is a multiple of } 5\}$,then $A - B$ is equal to,(where $\bar{B}$ is the complement of set $B$.)

A
$\bar{A} \cap B$
B
$A \cap \bar{B}$
C
$\bar{A} \cap \bar{B}$
D
$\overline{A \cap B}$

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Class 11

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Set Theory

Subtopic

Complement of a Set

If $P(A) = 0.25$,$P(B) = 0.50$,and $P(A \cap B) = 0.14$,then what is the value of $P(A \cap \overline{B})$?

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Let $U = \{1, 2, 3, 4, 5, 6\}$,$A = \{2, 3\}$,and $B = \{3, 4, 5\}$. Find $A'$,$B'$,$A' \cap B'$,$A \cup B$,and hence show that $(A \cup B)' = A' \cap B'$.

Easy

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For each positive real number $\lambda$,let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin(\sqrt{n+1}) - \sin(\sqrt{n})| < \lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

KVPY 2016

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If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

Medium

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Let $U$ be the set of all triangles in a plane. If $A$ is the set of all triangles with at least one angle different from $60^{\circ},$ what is $A^{\prime}$?

Easy

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If $A = \{x : x \text{ is a multiple of } 3\}$ and $B = \{x : x \text{ is a multiple of } 5\}$,then $A - B$ is equal to,(where $\bar{B}$ is the complement of set $B$.)

Similar Questions

If $P(A) = 0.25$,$P(B) = 0.50$,and $P(A \cap B) = 0.14$,then what is the value of $P(A \cap \overline{B})$?

Let $U = \{1, 2, 3, 4, 5, 6\}$,$A = \{2, 3\}$,and $B = \{3, 4, 5\}$. Find $A'$,$B'$,$A' \cap B'$,$A \cup B$,and hence show that $(A \cup B)' = A' \cap B'$.

For each positive real number $\lambda$,let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin(\sqrt{n+1}) - \sin(\sqrt{n})| < \lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

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