Q16 of 18 Page 13

Show that the following statement is true by the method of contra positive.


p: If x is an integer and x2 is even, then x is also even.
Let x be not even i.e. Let x = 2n + 1.
Therefore, x2 = (2n + 1)2 = 4n2 + 4n + 1 = 4(n2 + n) + 1.
Thus 4(n2 + n) + 1 is odd.
i.e. If q is not true, then p is not true, is proved.
Hence the given statement is not true.

More from this chapter

All 18 →
14
Show that the statement p: "If x is a real number such that x3 + 4x = 0, then x is 0" is true by

(i) Direct method.

(ii) Method of contradiction.

(iii) Method of contra positive.

15
Show that the statement "For any real number a and b, a2 = b2 implies that a = b" is not true by giving a counter example.

17
By giving a counter example, show that the following statements are not true.

(i) p: If all the angles of a triangle are equal then the triangle is not obtuse angled triangle.

(ii) q: The equation x2 – 1 = 0 does not have root lying between 0 and 2.

18
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 bisects 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: is a rational number.