Set Theory Algebra

Step 1: Check each option.
- Option (i): $%5Cexists%20x%20%5Cin%20A$ such that $x%20%2B%203%20%3D%208$ . This is true for $x%20%3D%205$ , since $5%20%2B%203%20%3D%208$ . - Option (ii): $%5Cexists%20x%20%5Cin%20A$ such that $x%20%2B%202%20%3C%209$ . This is true for $x%20%3D%201%2C%202%2C%203%2C%204$ , as $1%20%2B%202%20%3D%203$ , $2%20%2B%202%20%3D%204$ , $3%20%2B%202%20%3D%205$ , $4%20%2B%202%20%3D%206$ . - Option (iii): $%5Cforall%20x%20%5Cin%20A%2C%20x%20%2B%206%20%5Cgeq%209$ . This is false. For $x%20%3D%201$ , $1%20%2B%206%20%3D%207$ , which is less than 9. Hence, this is not true for all $x$ . - Option (iv): $%5Cexists%20x%20%5Cin%20A$ such that $x%20%2B%206%20%3C%2010$ . This is true for $x%20%3D%201%2C%202$ , since $1%20%2B%206%20%3D%207$ and $2%20%2B%206%20%3D%208$ .

Step 2: Conclude.
The statement in option (iii) is not true, as there exists at least one $x$ (i.e., $x%20%3D%201$ ) for which $x%20%2B%206%20%3C%209$ .

Final Answer: $%5Cboxed%7B(iii)%20%5C%3B%20%5Cforall%20x%20%5Cin%20A%2C%20%5C%3B%20x%20%2B%206%20%5Cgeq%209%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Set Theory Algebra

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs