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Intersection of Sets

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☼ Intersection of Sets : The intersection of two sets A and B, denoted by A B is the set of all those elements which are common to both A and B.

Thus, A $\cap$ B = { x : x $\in$ A and x $\in$ B }.

Clearly, x $\in$ A $\cap$ B $\Rightarrow$ x $\in$ A and x $\in$ B.

and, x $\notin$ A $\cap$ B $\Rightarrow$ x $\notin$ A or x $\notin$ B.

e.g. (i) If A = { a, b, c, d } and B = { b, d, e, f }, then A $\cap$ B = { b, d }.

(ii) If A = { x : x $\in$ N, x is multiple of 10 }

and B = { x : x $\in$ N, x is a multiple of 15 }, then

A $\cap$ B = { x : x $\in$ N, x is a multiple of 30 }.

Note that L.C.M. of 10 and 15 is 30.

Keep in Mind : In mathematics,

$\cup$ = or = + = v = Upper Bound

$\cap$ = and = $\times$ = ^ = Lower Bound = L. C. M.