Ace booklet questions no 07

Question

If A∆B = (A intersection B) whole complement than the universal set is??

Comments

A ∆ B = ( A U B ) - ( A ∩ B )

Given that

A ∆ B = ( A ∩ B )'  = U - ( A ∩ B ) ====> Universal Set is ( A U B )

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The universal set should be  $A \bigcup B$.

Explanation:

We know, $A \Delta B =\left ( A \bigcup B \right ) - \left ( A \bigcap B \right )$

$A \Delta B = \left ( A \bigcap B \right )'$ = Universal Set - $\left ( A \bigcap B \right )$

$\left ( A \bigcup B \right ) - \left ( A \bigcap B \right )$ = Universal Set - $\left ( A \bigcap B \right )$

=> Universal Set =  $\left ( A \bigcup B \right ) $

Answer 1

Given that A∆B= ( A meet B)'= UNIVERSAL SET - (A meet B)

By definition A∆ B= ( AUB)-( A meet B)

HHence A∆ B is Universal set.