(C) Using De Morgan's Law,we know that $(A \cup B)' = A' \cap B'$.Therefore,$A \cap (A \cup B)' = A \cap (A' \cap B')$.By the associative law of sets,

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(C) Using De Morgan's Law,we know that $(A \cup B)' = A' \cap B'$.Therefore,$A \cap (A \cup B)' = A \cap (A' \cap B')$.By the associative law of sets,this can be rewritten as $(A \cap A') \cap B'$.Since $A \cap A' = \phi$,we have $\phi \cap B' = \phi$.Thus,$A \cap (A \cup B)' = \phi$.

Class 11 Mathematics Set Theory Complement of a Set

Medium

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

A
$A$
B
$B$
C
$\phi$
D
None of these

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Set Theory

Subtopic

Complement of a Set

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{1, 2, 3, 4\}$,$B = \{2, 4, 6, 8\}$,and $C = \{3, 4, 5, 6\}$. Find $B^{\prime}$.

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The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

MediumAP EAMCET 2009

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Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$,$A = \{ 1, 2, 5 \}$,and $B = \{ 6, 7 \}$. Then $A \cap B'$ is:

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If $\frac{2}{11}$ is the probability of an event $A$,what is the probability of the event 'not $A$'?

Easy

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Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$,$A = \{1, 2, 5\}$,and $B = \{6, 7\}$. Find $A \cap B'$.

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

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Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{1, 2, 3, 4\}$,$B = \{2, 4, 6, 8\}$,and $C = \{3, 4, 5, 6\}$. Find $B^{\prime}$.

The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$,$A = \{ 1, 2, 5 \}$,and $B = \{ 6, 7 \}$. Then $A \cap B'$ is:

If $\frac{2}{11}$ is the probability of an event $A$,what is the probability of the event 'not $A$'?

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