Let A = 1, 2 , B = 1, 2, 3, 4 , C = 5, 6 and D = 5, 6, 7, 8 . Ver… - Vidyadip

Question

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
$\text{A}\times\text{C}\subset\text{B}\times\text{D}$

✓

Answer

We have,
A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
$\therefore$ B × D = {1, 2, 3, 4} × {5, 6, 7, 8}
{(1, 5), (1, 6), (1, 7), (1, 8) , (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)} ....(i)
and, A × C = (1, 2) × (5, 6)
= {(1, 5), (1, 6), (2, 5), (2, 6)} ....(ii)
Clearly from equation (i) and equation (ii), we get
$\text{A}\times\text{C}\subset\text{B}\times\text{D}$
Hence verified.

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