Given: A'⊂ B Using De morgan's law: (A∩ B')'=A'∪ (B')'=A'∪ B Since, A'⊂ B⇒ A'∪ B=B ⇒ (A∩ B')'=A'∪ B=B ...

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Standard IX

Mathematics

Application on Cardinality of 2 Sets

If A'⊂ B, the...

Question

If $A^{'} \subset B,$ then $(A \cap B^{'})^{'} =$

B

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A^{'}

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A

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B^{'}

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Solution

The correct option is A $B$
Given: $A^{'} \subset B$
Using De - morgan's law:
$(A \cap B^{'})^{'} = A^{'} \cup (B^{'})^{'} = A^{'} \cup B$
Since, $A^{'} \subset B \Rightarrow A^{'} \cup B = B$
$\Rightarrow (A \cap B^{'})^{'} = A^{'} \cup B = B$

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If A′⊂B, then (A∩B′)′=

The correct option is A BGiven: A′⊂B Using De - morgan's law: (A∩B′)′=A′∪(B′)′=A′∪B Since, A′⊂B⇒A′∪B=B ⇒(A∩B′)′=A′∪B=B

If $A^{'} \subset B,$ then $(A \cap B^{'})^{'} =$

The correct option is A $B$
Given: $A^{'} \subset B$
Using De - morgan's law:
$(A \cap B^{'})^{'} = A^{'} \cup (B^{'})^{'} = A^{'} \cup B$
Since, $A^{'} \subset B \Rightarrow A^{'} \cup B = B$
$\Rightarrow (A \cap B^{'})^{'} = A^{'} \cup B = B$