Q.If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respectively, then verify that [A-(B∪C)] = [(A-B)∩(A-C)].

List the distinct letters in each word: A = letters of 'college' = {c,o,l,e,g} (n(A)=5). B = letters of 'marriage' = {m,a,r,i,g,e} (n(B)=6). C = letters of 'luggage' = {l,u,g,a,e} (n(C)=5). First, $B \cup C = \{m,a,r,i,g,e,l,u\}$. Then $A-(B\cup C)$ removes from A every letter also in $B\cup C$: from A={c,o,l,e,g}, the letters l, e, g are all in $B\cup C$, so what remains is $\{c,o\}$. Now the right side: $A-B = \{c,o,l,e,g\}-\{m,a,r,i,g,e\} = \{c,o,l\}$ (removing e and g, which are in B). $A-C = {c,o,l,e,g} …

Write each word's set of distinct letters, compute the left side (A minus the union of B and C) and the right side (intersection of th …

Do not forget that repeated letters within a single word (like the two g's in 'luggage' or the two e's in ' …