Question

If A = {a,b}, B = {b,c} and C = {b,c,d} ; then A $\times$ (B $\cup$ C) = _____ .

• A. (A $\times$ B) $\cup$ (A $\times$ C)
• B. (A $\cup$ B) $\cup$ C
• C. (A $\cup$ B) $\times$ C
• D. (A $\cap$ B) $\times$ C

Answer 1

The correct option is A (A $\times$ B) $\cup$ (A $\times$ C)

Let us write the set of (B $\cup$ C) first.
(B $\cup$ C) = {b,c,d}
A $\times$ (B $\cup$ C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)}
Now Let us verify the given options :

(a) A $\cup$ B = {a,b,c}
(A $\cup$ B) $\times$ C = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d),(c,b),(c,c),(c,d)}

(b) A $\cap$ B = {b}
(A $\cap$ B) $\times$ C = {(b,b),(b,c),(b,d)}

(c) A $\cup$ B = {a,b,c}
(A $\cup$ B) $\cup$ C = {a,b,c,d}

(d) (A $\times$ B) = {(a,b),(a,c),(b,b),(b,c)}
(A $\times$ C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)}
(A $\times$ B) $\cup$ (A $\times$ C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)} which is equal to
A $\times$ (B $\cup$ C)