## Solving Lesson 11 Page 9 Math Workbook 10 – Kite>

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 $$2024 = 4.506$$)