**Topic**

State the negative statements of each of the following statements and determine whether each of them is true or false:

a) A: “The axis of symmetry of the graph of the function \(y = – {x^2}\) is the vertical axis”

b) B: “Equation \(3{x^2} + 1 = 0\) has a solution”

c) C: “Two lines \(y = 2x + 1\) and \(y = – 2x + 1\) are not parallel”

d) D: “The number 2024 is not divisible by 4”

**Solution method – See details**

The negation of proposition P is “Not P”, denoted \(\overline P \)

+ P is true then \(\overline P \) is false

+ P is false then \(\overline P \) is true

**Detailed explanation**

a) \(\overline A \): “Axis of symmetry of the function graph \(y = – {x^2}\) **Not** is the vertical axis”

A is true so \(\overline A \) is false.

b)\(\overline B \): “Equation \(3{x^2} + 1 = 0\) has no solution”

B is false, \(\overline B \) is true (because \(3{x^2} + 1 \ge 1 > 0\))

c) \(\overline C \): “Two lines \(y = 2x + 1\) and \(y = – 2x + 1\) are parallel to each other”

C is true, \(\overline C \) is false.

d) \(\overline D \): “The number 2024 is divisible by 4”

D is false, \(\overline D \) is true (because \(2024 = 4.506\))