The A- B- C - A- B C - C C C - C c is equal to

The correct option is C B ∩ C ^ C (A∩ B^C∩ C^C)^C=(A (A∩ B) (A∩ C))^C =(A^C∪(A∩ B)∪(A∩ C)) (A∩ B^C∩ C^C)^C∩ C^C=(A^C∪ (B∪ C))∩ C^C =B∩ ...

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Byju's Answer

Standard XII

Mathematics

Properties of Set Operation

The A∪ B∪ C...

Question

The $(A \cup B \cup C) \cap {(A \cap B^{C} \cap C^{C})}^{C} \cap C^{c}$ is equal to

B^{C} \cap C^{C}

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A \cap C

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B \cap C^{C}

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C \cap C^{C}

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Solution

The correct option is C $B \cap C^{C}$
$(A \cap B^{C} \cap C^{C})^{C} = (A - (A \cap B) - (A \cap C))^{C}$
$= (A^{C} \cup (A \cap B) \cup (A \cap C))$
$(A \cap B^{C} \cap C^{C})^{C} \cap C^{C} = (A^{C} \cup (B \cup C)) \cap C^{C}$
$= B \cap C^{C}$
$(A \cup B \cup C) \cap (B \cap C^{C}) ⋂ C^{c} = B \cap C^{C}$

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The (A∪B∪C)∩(A∩BC∩CC)C∩Cc is equal to

The correct option is C B∩CC(A∩BC∩CC)C=(A−(A∩B)−(A∩C))C=(AC∪(A∩B)∪(A∩C))(A∩BC∩CC)C∩CC=(AC∪(B∪C))∩CC=B∩CC(A∪B∪C)∩(B∩CC)⋂Cc=B∩CC

The $(A \cup B \cup C) \cap {(A \cap B^{C} \cap C^{C})}^{C} \cap C^{c}$ is equal to