Question

8. Which of the following is the empty set? A.{x:x is a real number and x²-1=0}

B. {x:x E R and x²+1=0}
C.{x:x is a real number and x²-9=0}
D.{x:x E R and x²=x+2}​

Answer 1

The empty set is a set with no elements.

Option A: {x: x is a real number and x² - 1 = 0} is not the empty set because it contains two elements: 1 and -1, which are the solutions of the equation x² - 1 = 0.

Option B: {x: x E R and x² + 1 = 0} is also not the empty set because it contains no real numbers, but it does contain imaginary numbers. The solutions of the equation x² + 1 = 0 are +i and -i, where i is the imaginary unit.

Option C: {x: x is a real number and x² - 9 = 0} is not the empty set because it contains two elements: 3 and -3, which are the solutions of the equation x² - 9 = 0.

Option D: {x: x E R and x² = x + 2} is not the empty set because it contains two elements: 2 and -1, which are the solutions of the equation x² = x + 2.

Therefore, the correct answer is none of the given options.