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Some More Important Results

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☼ Some More Important Results :

(i) A $\cup$ B = $\emptyset$ $\large \Leftrightarrow$ A = $\emptyset$ and B = $\emptyset$ .

(ii) A – B = $\emptyset$ $\large \Leftrightarrow$ A $\subseteq$ B.

(iii) A – B = A $\cap$ B ٰ = A – ( A $\cap$ B )

(iv) A $\subseteq$ B $\large \Leftrightarrow$ B ٰ $\subseteq$ A ٰ.

(v) A – ( B $\cup$ C ) = ( A – B ) $\cap$ ( A – C ).

(vi) A – ( B $\cap$ C ) = ( A – B ) $\cup$ ( A – C ).

(vii) A $\cap$ ( B – C ) = ( A $\cap$ B ) – ( A $\cap$ C ).

(vii) A $\cup$ ( B – C ) = ( A $\cup$ B ) – ( A $\cup$ C ).