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H Harsh Kankaria
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.  

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H Harsh Kankaria
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.   

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H Harsh Kankaria
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.  

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.

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H Harsh Kankaria
The given statement in the form “if-then” is : If diagonals of a quadrilateral bisect each other, then it is a parallelogram.  

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H Harsh Kankaria
The given statement in the form “if-then” is : If the Banana tree stays warm for a month, then it will bloom.   

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H Harsh Kankaria
The given statement in the form “if-then” is : If you get a job, then your credentials are good.  

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H Harsh Kankaria
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.

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H Harsh Kankaria
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.  

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H Harsh Kankaria
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 .  

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H Harsh Kankaria
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.  

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H Harsh Kankaria
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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