For any sets A and B- prove that-i A -A - B-Aii A - A - B - A

(i) Since (A∩ B)⊆ A, we have A∪ (A∩ B)=A[∵ X ⊆ Y ⇒ X∪ Y=Y] (ii) Since A⊆ (A∪ B), we have A∩ (A∪ B)=A[∵ X ⊆ Y ⇒ X∩ Y=X] ...

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Fundamental Laws of Logarithms

For any sets ...

Question

For any sets A and B, prove that:
$(i) A \cup (A \cap B) = A$

$(i i) A \cap (A \cup B) = A$

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A \cup (A \cap B) = A

A \cap (A \cup B) = A

(Idempotent laws) For any set A, prove that:
$(i) A \cup A = A$

$(i i) A \cap A = A$

A' \cup B = U \Rightarrow A \subset B

B' \subset A' \Rightarrow A \subset B

(De Morgan's laws) For any two sets A and B, prove that:
$I . (A \cup B)^{'} = (A^{'} \cap B^{'})$

$I I . (A \cap B)^{'} = (A^{'} \cup B^{'})$

(Commultative laws) For any two sets a and B, prove that:
$I . A \cup B = B \cup A$ [Commutative law for union of sets]

$I I . A \cap B = B \cap A$ [Commutative law for intersection of sets]

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