Blog

Difference of Sets

No Comments

☼ Difference of Sets : For any two sets A and B, we define :

A – B = { x : x $\in$ A and x $\notin$ B }

A – B = A – ( A $\cap$ B )

e.g. (i) If A = { 2, 3, 5, 7, 11 } and B = { 5, 7, 11, 13, 17 }, then

A – B = A – ( A $\cap$ B )

= { 2, 3, 5, 7, 11 } – { 5, 7, 11 }

= { 2, 3 }

B – A = B – ( A $\cap$ B )

= { 5, 7, 11, 13, 17 } – { 5, 7, 11 }

= { 13, 17 }

Note: (i) A $\subseteq$ B $\Rightarrow$ A – B = $\emptyset$ .

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