Question

If A = {x $\in$ N | 1 < x < 4},
B = {x $\in$ W | 0 $\le$ x < 2}
and C = {x $\in$ N | x < 3}.
Find (A $\times$ B) $\cup$ (A $\times$ C)

• A. {(2,0),(2,1),(3,0),(3,1)}
• B. {(0,2),(1,2),(2,2),(0,3),(1,3),(2,3)}
• C. {(2,0),(2,1),(2,2),(3,0),(3,1),(3,2)}
• D. {(2,1),(2,2),(3,1),(3,2)}

Answer 1

The correct option is C {(2,0),(2,1),(2,2),(3,0),(3,1),(3,2)}

Given, A = {x $\in$ N | 1 < x < 4}
= {2,3}
B = {x $\in$ W | 0 $\le$ x < 2}
= {0,1}
C = {x $\in$ N | x < 3}
= {1,2}
$\therefore$ A$\times$B = {2,3} $\times$ {0,1}
= {(2,0),(2,1),(3,0),(3,1)}
A$\times$C = {2,3} $\times$ {1,2}
= {(2,1),(2,2),(3,1),(3,2)}
$\therefore$ (A×B) $\cup$ (A×C) = {(2,0),(2,1),(3,0),(3,1)} $\cup$ {(2,1),(2,2),(3,1),(3,2)}
= {(2,0),(2,1),(2,2),(3,0),(3,1),(3,2)}