Express the set $\{x : x ext{ is a positive integer and } x^{2}

Question

Express the set $\{x : x 	ext{ is a positive integer and } x^{2} < 40\}$ in roster form.

Accepted Answer

B. $\{1, 2, 3, 4, 5, 6\}$

We need positive integers $x$ with $x^{2} < 40$.
Check each: $1^{2} = 1$, $2^{2} = 4$, $3^{2} = 9$, $4^{2} = 16$, $5^{2} = 25$, $6^{2} = 36$, $7^{2} = 49$.
Values $1$ through $6$ satisfy $x^{2} < 40$; $7^{2} = 49 > 40$, so $7$ is excluded.
Roster form: $\{1, 2, 3, 4, 5, 6\}$.
- Trap A stops at $5$ (misses $6$).
- Trap C includes $7$ (overshoots).
- Trap D omits $1$ (forgets that $1$ is a positive integer).
This is NCERT Class 11, Example 2.

Answer

$\{1, 2, 3, 4, 5\}$

Answer

$\{1, 2, 3, 4, 5, 6, 7\}$

Answer

$\{2, 3, 4, 5, 6\}$

Express the set $\{x : x \text{ is a positive integer and } x^{2} < 40\}$ in roster form.