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 $C = \{17, 26, 35, 44, 53, 62, 71, 80\}$.
Explore More
Similar Questions
If $Q = \{x : x = \frac{1}{y}, \text{ where } y \in N\}$,then which of the following is true?
Easy
View SolutionLet $S = \{1, 2, 3, \ldots, n\}$ and $A = \{(a, b) \mid 1 \leq a, b \leq n\} = S \times S$. $A$ subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then,the number of good subsets of $A$ is
Let $A = \{ \theta : \sin(\theta) = \tan(\theta) \}$ and $B = \{ \theta : \cos(\theta) = 1 \}$ be two sets. Then
DifficultJEE MAIN 2013
View SolutionMake correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is an equilateral triangle in a plane} } \dots { x:x \text{ is a triangle in the same plane} }$
${ x:x \text{ is an equilateral triangle in a plane} } \dots { x:x \text{ is a triangle in the same plane} }$
Medium
View SolutionExamine whether the following statement is true or false:
${1, 2, 3} \subset {1, 3, 5}$
${1, 2, 3} \subset {1, 3, 5}$
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo