# Q&A - Ask Doubts and Get Answers

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The statement is False.  A chord is a line segment intersecting the circle in two points. But it is not necessary for a chord to pass through the centre.
The statement is False. By definition, A chord is a line segment intersecting the circle in two points. But a radius is a line segment joining any point on circle to its centre.
Given, The equation does not have a root lying between 0 and 2. Let x = 1 Hence 1 is a root of the equation . But 1 lies between 0 and 2. Hence the given statement is not true.
We know, Sum of all the angles of a triangle = If all the three angles are equal, then each angle is  But  is not an obtuse angle, and hence none of the angles of the triangle is obtuse. Hence the triangle is not an obtuse-angled triangle. Hence the given statement is not true.
Given, If x is an integer and is even, then is also even.  Let, p : x is an integer and is even q:  is even In order to prove the statement “if p then q”  Contrapositive Method:  By assuming that q is false, prove that p must be false. So, q is false: x is not even  x is odd  x = 2n+1 (n is a natural number) Hence  is odd  is not even  Hence p is false. Hence the given statement is true.
Given, For any real numbers a and b,  implies that . Let a = 1 & b = -1 Now, = 1  = 1 But a  b Hence  does not imply that . Hence the given statement is not true.
If is a real number such that , then is 0 : (if p then q) p: x is a real number such that . q: x is 0. In order to prove the statement “if p then q”  Contrapositive Method:  By assuming that q is false, prove that p must be false. So, q is false:   x.(Positive number)  0.(Positive number) Therefore p is false.
If is a real number such that , then is 0 : (if p then q) p: x is a real number such that . q: x is 0. In order to prove the statement “if p then q”  Contradiction:  By assuming that p is true and q is false. So, p is true:  There exists a real number x such that  q is false:  Now,  Hence, x = 0 But we assumed . This contradicts our assumption. Therefore q is true.
If is a real number such that , then is 0 : (if p then q) p: x is a real number such that . q: x is 0. In order to prove the statement “if p then q”  Direct Method:  By assuming that p is true, prove that q must be true. So, p is true:There exists a real number x such that  Hence, x = 0 Therefore q is true.
If a quadrilateral is a parallelogram, then its diagonals bisect each other.  (if p then q) The Contrapositive is (~q, then ~p) Hence (i) is the Contrapositive statement. The Converse is (q, then p) Hence (ii) is the Converse statement.
If you live in Delhi, then you have winter clothes. : (if p then q) The Contrapositive is (~q, then ~p) Hence (i) is the Contrapositive statement. The Converse is (q, then p) Hence (ii) is the Converse statement.
The given statement in the form “if-then” is : (iv) If you get A+ in the class, then you have done all the exercises in the book.
The given statement in the form “if-then” is : If diagonals of a quadrilateral bisect each other, then it is a parallelogram.
The given statement in the form “if-then” is : If the Banana tree stays warm for a month, then it will bloom.
The given statement in the form “if-then” is : If you get a job, then your credentials are good.
First, we convert the given sentence into the "if-then" statement: If x is an even number, then x is divisible by 4. The contrapositive is: If x is not divisible by 4, then x is not an even number. The converse is: If x is divisible by 4, then x is an even number.
The contrapositive is: If you know how to reason deductively, then you can comprehend geometry. The converse is: If you do not know how to reason deductively, then you cannot comprehend geometry.
The contrapositive is: If something is not at low temperature, then it is not cold. The converse is: If something is at low temperature, then it is cold .
The contrapositive is:  If two lines intersect in the same plane, then they are not parallel. The converse is: If two lines do not intersect in the same plane, then they are parallel.
The contrapositive is : If a number x is not odd, then x is not a prime number. The converse is : If a number x in odd, then it is a prime number.
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