MATHS (Each question 1 marks)

If the Banana tree stays warm for a month, then it will bloom.

The day that is being referred to is not evident from the sentence. Hence, it is not a statement.

This sentence is subjective in the sense that for some people, mathematics can be easy and for some others, it can be difficult. Hence, it is not a statement.

If you get a job, then your credentials are good.

This is not the same as statement. Thus, the given statements are not the negation of each other.

It is an order. Therefore, it is not a statement.

Chennai is not the capital of Tamil Nadu.

The negation of the first statement is “the number x is not a rational number”. This means that the number x is an irrational number, which is the same as the second statement. Therefore, the given statements are negations of each other.

Statement r can be written as follows. If you can access the website, then you pay a subscription fee.

This sentence is sometimes correct and sometimes incorrect. For example, the square of 2 is an even number. However, the square of 3 is an odd number. Hence, it is not a statement.

Every natural number is not an integer.

The given statement p is false. According to the definition of chord, it should intersect the circle at two distinct points.

Statement p can be written as follows. If you log on to the server, then you have a password.

The product of (–1) and 8 is (–8). Therefore, the given sentence is incorrect. Hence, it is a statement.

The given statement q is false. If the chord is not the diameter of the circle, then the centre will not bisect that chord. In other words, the centre of a circle only bisects the diameter, which is the chord of the circle.

You get an A grade if and only if you do all the homework regularly.

A quadrilateral is equiangular if and only if it is a rectangle.

The negation of statement q is as follows. There exists a cat that does not scratch.

Statement q can be written as follows. If it rains, then there is a traffic jam.

The negation of statement s is as follows. There does not exist a number x, such that 0 < x < 1.

The quantifier is “There exists”. The negation of this statement is as follows. There exists a state in India which does not have a capital.

The quantifier is “For every”. The negation of this statement is as follows. There exist a real number x such that x is not less than x + 1.

The number 2 is not greater than 7.

The negation of statement r is as follows. There exists a real number x, such that neither x > 1 nor x < 1.

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Here, “or” is inclusive since a person can have both a ration card and a passport to apply for a driving license.

You watch television if and only if your mind is free.

x > y ⇒ –x < –y (By a rule of inequality) Thus, the given statement s is true.

Here, “or” is exclusive because it is not possible for the Sun to rise and the moon to set together.

The negation of the first statement is “the number x is a rational number”. This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number. Therefore, the given statements are negations of each other.

Here, “or” is exclusive because all integers cannot be both positive and negative.

All real numbers can be written as a × 1 + 0 × i. Therefore, the given sentence is always correct. Hence, it is a statement.

The sum of 5 and 7 is 12, which is greater than 10. Therefore, this sentence is always correct. Hence, it is a statement.

This sentence is sometimes correct and sometimes incorrect. For example, squares and rhombus have sides of equal lengths. However, trapezium and rectangles have sides of unequal lengths. Hence, it is not a statement.

All triangles are equilateral triangles.

The negation of statement is as follows. There exists real number x and y for which x + y ≠ y + x.

This sentence is incorrect because the maximum number of days in a month is 31. Hence, it is a statement.

The quantifier is “There exists”. The negation of this statement is as follows. There does not exist a number which is equal to its square.

This sentence is correct and hence, it is a statement.

The negation of statement p is as follows. There exists a positive real number x, such that x – 1 is not positive.