Question

11. Which of the following is a null ( or empty) set?
(A) { x:x is a natural number and x2 + 1 = 10 }
(B) { x:x is a natural number and x2 = 121 }
(C) { x:x is a natural number and x2 = – 10 }
(D) { x:x is a natural number and x2 ≤ 100 }

Answer 1

Step-by-step explanation:

$(A) \: \: \: {x}^{2} + 1 = 10 \\ \: \: \: \: \: {x}^{2} = 10 - 1 \\ \: \: \: \: {x}^{2} = 9 \\ \: \: \: x = \sqrt{9} \\ \: \: \: \: x = \underline{ \underline{ 3}} \\ \\ (B) \: \: \: {x}^{2} = 121 \\ \: \: \: \: x = \sqrt{121} \\ \: \: \: \: x = \underline{ \underline{ 11}} \\ \\ (C) \: \: \: {x}^{2} = -10 \\ \: \: \: \: x = \sqrt{ - 10} \\ \: \: \: - 10 \: \: is \: \: not \: \: a \: \: perfect \: \: square \\ It \: \: is \: \: a \: \: null \: \: set \\ \\ (D) \: \: \: {x}^{2} \leqslant 100 \\ \: \: \: \: x \leqslant \sqrt{100} \\ \: \: \: \: \underline{ \underline{ x \leqslant 10}}$