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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De Morgan's Laws

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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State, Whether the following statements are true of false.

(i) If $a < b, t h e n a - c < b - c$

(ii) If $a > b, t h e n a + c > b + c$

(iii) If $a < b, t h e n a c > b c$

(iv) If $a > b, t h e n \frac{a}{c} < \frac{b}{c}$

(v) If $a - c > b - d; t h e n a + d > b + c$

(vi) If $a < b, a n d c > 0, t h e n a - c > b - c where a, b, c and are real numbers and c \neq 0.$

| \to a + \to b | = | \to a - \to b |

| \to a \times \to b |

| \to a | = 3

| \to b | = 1

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