Class 11th Maths Textbook Chapter 1: Sets Exercise 5: Complement of a Set Question 3 (xi) Solution

Question

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (xi) {x : x $\in$ N and 2x + 1 $>$ 10}

Accepted Answer

Simplify the inequality (2x + 1 $>$ 10) by moving the constants to one side.
 	ext{2x > 10 - 1}|||	ext{2x > 9} Find the elements of the set by solving the inequality from Step 1.
 	ext{x > 9 / 2}|||	ext{Therefore, Set = \{x : x $\in$ N, x > 9 / 2\}} Find the complement of the given set by finding the elements of the universal set of natural{math_tip:def_natural_number} numbers that are not elements of the given set.
 {green}	extbf{Answer: \{x : x $\in$ N, x $\leq$ (9 / 2)\} or \{1, 2, 3, 4\}}|||	extbf{Reason: The set contains all natural numbers that are greater than 9 / 2. Therefore, its complement consists of all natural numbers that are less than or equal to 9 / 2.}{/green}

Question: 3 (xi)

Answer