-A- B- C- -A - C- is equivalent to

The correct option is C A' ∩ C' {[(A' ∩ B')' ∪ C] ∩ (A ∪ C)}' = {[((A ∪ B)')' ∪ C] ∩ (A ∪ C)}' = {[(A ∪ B) ∪ C] ∩ (A ∪ C)}' = {[A ∪ B ∪ C] ∩ (A ∪ C)}' = {[B ∪ ...

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Byju's Answer

Standard VIII

Mathematics

Complement of a Set

[A'∩ B''∪ C] ...

Question

${[(A^{'} \cap B^{'})^{'} \cup C] \cap (A \cup C)}^{'}$ is equivalent to

$A \cap C$

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$A^{'} \cap C$

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$A^{'} \cap C^{'}$

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$A \cup B^{'}$

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Solution

The correct option is C
$A^{'} \cap C^{'}$

${[(A^{'} \cap B^{'})^{'} \cup C] \cap (A \cup C)}^{'}$

$= {[((A \cup B)^{'})^{'} \cup C] \cap (A \cup C)}^{'}$

$= {[(A \cup B) \cup C] \cap (A \cup C)}^{'}$

$= {[A \cup B \cup C] \cap (A \cup C)}^{'}$

$= {[B \cup (A \cup C)] \cap (A \cup C)}^{'}$

$= (A \cup C)^{'}$

$= A^{'} \cap C^{'}$

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{[(A′∩B′)′∪C]∩(A∪C)}′ is equivalent to

The correct option is C A′∩C′ {[(A′∩B′)′∪C]∩(A∪C)}′ ={[((A∪B)′)′∪C]∩(A∪C)}′ ={[(A∪B)∪C]∩(A∪C)}′ ={[A∪B∪C]∩(A∪C)}′ ={[B∪(A∪C)]∩(A∪C)}′ =(A∪C)′ =A′∩C′

${[(A^{'} \cap B^{'})^{'} \cup C] \cap (A \cup C)}^{'}$ is equivalent to