Question

If $A = \{1,2,3,5\}$ and $B = \{4,6,9\}$, we define a relation $R$ from $A$ to $B$ by $R = \{(x, y) :$ the difference between $x$ and $y$ is odd $: x \in A$, $y \in B\}$, then $R$ in roster form is

• A. $\{(1,1), (4,4), (7,4), (4,7), (7, 7)\}$
• B. $\{(1,1), (4,4), (4,7), (7,4), (7,7), (3,3)\}$
• C. $\{(1,5), (1,6), (3,6)\}$
• D. $\{(1,4), (1,6), (2,9), (3,4), (3,6), (5,4), (5,6)\}$

Answer 1

Answer: (D)

Here, $A = \{1,2,3,5\}$ and $B = \{4,6, 9\}$, $x \in A$, $y \in B$
$\therefore x - y = (1 - 4), (1 - 6), (1 - 9), (2 - 4), (2 - 6), (2 - 9)$,
$(3 - 4), (3 - 6), (3 - 9), (5 - 4), (5 - 6), (5 - 9)$
$x - y = -3, -5, -8, -2, -4, -7, -1, -3, -6,1, -1, -4$
$\therefore R = \{(1,4), (1,6), (2,9), (3,4), (3,6), (5,4), (5,6)\}$