(i) p : For every positive real number x, the number (x – 1) is also positive.
The negation of the statement:
p: For every positive real number x, the number (x – 1) is also positive.
is ~p: There exists a positive real number x, such that the number (x – 1) is not positive.
(ii) q: For every real number x, either x > 1 or x < 1.
The negation of the statement:
q: For every real number x, either x > 1 or x < 1.
is ~q: There exists a real number such that neither x>1 or x<1.
(iii) r: There exists a number x such that 0 < x < 1.
The negation of the statement:
r: There exists a number x such that 0 < x < 1.
is ~r: For every real number x, either x ≤ 0 or x ≥ 1.
Answered by Sakshi | 1 year agoDetermine whether the argument used to check the validity of the following statement is correct: p: “If x2 is irrational, then x is rational.” The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.
Which of the following statements are true and which are false? In each case give a valid reason for saying so
(i) p: Each radius of a circle is a chord of the circle.
(ii) q: The centre of a circle bisect each chord of the circle.
(iii) r: Circle is a particular case of an ellipse.
(iv) s: If x and y are integers such that x > y, then – x < – y.
(v) t: \( \sqrt{11}\) is a rational number.
By giving a counter example, show that the following statement is not true. p: “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”
Show that the following statement is true “The integer n is even if and only if n2 is even”
Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x2 is odd, then x is also odd.”