Question

If $A,B,C$ are the sets of the letters in the words college,marriage and luggage respectively, then verify that $[A-(B\cup C\left)\right]=\left[\right(A-B)\cap (A-C\left)\right]$

Answer 1

$A$ is the set of the letters in the word college.

$A=\left\{c,o,l,e,g\right\}$

$B$ is the set of the letters in the word marriage.

$B=\left\{m,a,r,i,g,e\right\}$

$C$ is the set of the letters in the word luggage.

$C=\left\{l,u,g,a,e\right\}$

$B\cup C=\left\{m,a,r,i,g,e,l,u\right\}$

$A-\left(B\cup C\right)=\left\{c,o\right\}$ (1)

$A-B=\left\{c,o,l\right\}$

$A-C=\left\{c,o\right\}$

$\left(A-B\right)\cap \left(A-C\right)=\left\{c,o\right\}$ (2)

From equation (1) and (2), $A-\left(B\cup C\right)=\left(A-B\right)\cap \left(A-C\right)$.