Relations

Question

Let R be a relation on the set N of natural numbers defined by R = {(x, y) : x + 2y = 8}. The range of R is

RankGuru · Accepted Answer

1. **Definition of Range**: The range is the set of all possible $y$-values from the ordered pairs $(x, y)$ that satisfy the relation.
2. **Constraint Check**: $x, y \in \mathbb{N}$ (natural numbers $\{1, 2, 3, \dots\}$).
3. **Test $y$ values**:
   - If $y = 1, x = 8 - 2(1) = 6 \in \mathbb{N}$. Valid.
   - If $y = 2, x = 8 - 2(2) = 4 \in \mathbb{N}$. Valid.
   - If $y = 3, x = 8 - 2(3) = 2 \in \mathbb{N}$. Valid.
   - If $y = 4, x = 8 - 2(4) = 0 
otin \mathbb{N}$. Invalid.
4. **Identify Range**: The set of valid $y$-values is **$\{1, 2, 3\}$**.

Rank Guru

Relations

Select the correct option:

Solution

🔒 Solution Hidden from View

More relations Practice Questions

For two positive numbers a and b, which of the following is always true?

Let R be a relation on the set N of natural numbers defined by nRm \u21Longleftrightarrow n is a fac...

If R is a relation from a finite set A having m elements to a finite set B having n elements, then t...

The minimum number of ordered pairs that must be added to the relation R = {(1, 2), (2, 3)} on the s...

If A = {a, b, c}, then the number of equivalence relations on A containing (a, b) is

The relation 'less than' on the set of real numbers R is

About This Question

Solution