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Laws of operations

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$\large \mapsto$ Commutative Laws :

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

$\large \mapsto$ Associative Laws :

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

$\large \mapsto$ Distributive Laws :

(i) Distributive of union over intersection

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

(ii) Distributive of intersection over union

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

$\large \mapsto$ De–Morgan’s Laws :

(i) ( A $\cup$ B ) ٰ = Aٰ $\cap$ B ٰ (ii) ( A $\cap$ B ) ٰ = A ٰ $\cup$ B ٰ .