Question

Using the given diagram, express the following sets in the terms of A and B.

(i) {a,d}

(ii) (a,d,c,f)

(iii) {a,d,c,f,g,h}

(iv) {a,d,g,h}

(v) {g,h}

Answer 1

(i) {a,d} = {a,b,e,d} - {b,c,e,f}

= A - B Ans.

(ii) {a,d,c,f} = (A $\cup$ B) - {b,e}

= (A $\cup$ B) - (A $\cap$ B) Ans.

Also {a,d,c,f} = (A - B) $\cup$ (B - A)

(iii) {a,d,c,f,g,h} = (A $\cap$ B)' Ans.

[$\because$ {b,e} = $A\cap B\therefore (A\cap B{)}^{\prime }$ = {a,d,c,f,g,h} ]

(iv) {a,d,g,h} = B' Ans.

[$\because$ {b,c,e,f}=B $\therefore$ B' = {a,d,g,h}]

(v) {g,h} = (A $\cup$B)' Ans.

[$\because A\cup B$ = {a,b,c,d,e,f} $\therefore (A\cup B{)}^{\prime }$ = {g,h}]