The given statement can be written in the form of ‘if then’ is given below
If a and b are real numbers such that a2 = b2, then a = b
Let p: a and b are real numbers such that a2 = b2
q: a = b
The given statement has to be proved false.
To show this, two real numbers, a and b, with a2 = b2 are required such that a ≠ b
Let us consider a = 1 and b = – 1
a2 = (1)2 = 1
and
b2 = (-1)2 = 1
Hence, a2 = b2
However, a ≠ b
Therefore, it can be concluded that the given statement is false.
Answered by Sudhanshu | 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.”