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 \(2024 = 4.506\))