Write the following set in roster form:
$C = \{ x : x \text{ is a two-digit natural number such that the sum of its digits is } 8 \}$
$C = \{ x : x \text{ is a two-digit natural number such that the sum of its digits is } 8 \}$
(N/A) The set $C$ consists of all two-digit natural numbers where the sum of the digits is $8$.
Let the two-digit number be $xy$,where $x \in \{1, 2, \dots, 9\}$ and $y \in \{0, 1, \dots, 9\}$.
We require $x + y = 8$.
Possible pairs $(x, y)$ are:
If $x=1, y=7 \implies 17$
If $x=2, y=6 \implies 26$
If $x=3, y=5 \implies 35$
If $x=4, y=4 \implies 44$
If $x=5, y=3 \implies 53$
If $x=6, y=2 \implies 62$
If $x=7, y=1 \implies 71$
If $x=8, y=0 \implies 80$
Thus,the set in roster form is $C = \{17, 26, 35, 44, 53, 62, 71, 80\}$.
Let the two-digit number be $xy$,where $x \in \{1, 2, \dots, 9\}$ and $y \in \{0, 1, \dots, 9\}$.
We require $x + y = 8$.
Possible pairs $(x, y)$ are:
If $x=1, y=7 \implies 17$
If $x=2, y=6 \implies 26$
If $x=3, y=5 \implies 35$
If $x=4, y=4 \implies 44$
If $x=5, y=3 \implies 53$
If $x=6, y=2 \implies 62$
If $x=7, y=1 \implies 71$
If $x=8, y=0 \implies 80$
Thus,the set in roster form is $C = \{17, 26, 35, 44, 53, 62, 71, 80\}$.
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