Let p: If x is an integer and x2 is even, then x is also even
Let q: x is an integer and x2 is even
r: x is even
By contrapositive method, to prove that p is true, we assume that r is false and prove that q is also false
Let x is not even
To prove that q is false, it has to be proved that x is not an integer or x2 is not even
x is not even indicates that x2 is also not even.
Hence, statement q is false.
Therefore, the given statement p is true
Answered by Abhisek | 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.”