Question

From the given diagram, find the elements of:

A - (B $\cap$ C) and (A - B) $\cup$ (A - C) and enter $1$ or $0$ respectively if the given relation holds True or False: A - (B $\cap$ C) = (A - B) $\cup$ (A - C).

Answer 1

$(B\cap C)$ will have the elements which are common among the elements written inside the circle of $B$ and of $C$.

$\Rightarrow (B\cap C)=$ { $c,e$ }

And $A-(B\cap C)$ will have the elements inside the circle drawn for $A$ but not among the elements of $(B\cap C)=$ { $c,e$ }.

So, $A-(B\cap C)=$ { $a,b,d$ } .....(1)

Now, $A-B=$ { $a,b$ }

And $A-C=$ { $a,d$ }

The union of two sets has the elements of both sets.

So, $(A-B)\cup (A-C)=$ { $a,b,d$ } .....(2)

From (1) and (2), we have

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

The relation holds True.

$\therefore$ Answer is 1.