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:\( \sqrt{11}\) is a rational number.
1 Answer
Solution :-
(i) Right answer is False.
Explanation:-
According to the definition of chord, it should intersect the circle at two distinct points.
(ii) Right answer is False.
Explanation:-
If the chord is not the diameter of the circle, then the centre will not bisect that chord.
(iii) Right answer is True.
Explanation:-
The equation of an ellipse is,
If we put a = b = 1, then we get
x2 + y2 = 1, which is an equation of a circle
Hence, circle is a particular case of an ellipse.
Therefore, statement r is true
(iv) Right answer is True.
Explanation:-
x > y
By a rule of inequality
-x < – y
Hence, the given statement s is true
(v) Right answer is False.
Explanation:-
11 is a prime number and we know that the square root of any prime number is an irrational number.
Therefore, \( \sqrt{11}\) is an irrational number. Thus, the given statement t is false.
Related Questions
Determine 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.”