Q4 of 18 Page 898

Write the negation of each of the following statements:

(i) Every natural number is greater than 0.


(ii) Both the diagonals of a rectangle are equal.


(iii) The sum of 4 and 5 is 8.


(iv) The number 6 is greater than 4.


(v) Every natural number is an integer.


(vi) The number -5 is a rational number


(vii) All cats scratch.


(viii) There exists a rational number x such that x2 = 3.


(ix) All students study mathematics at the elementary level.


(x) Every student has paid the fees.


(xi) There is some integer k for which 2k = 6.


(xii) None of the students in this class has passed.


(i) The negation of the given statement is:


It is false that every natural number is greater than 0.


(Or)


Every natural number is not greater than 0.


(Or)


There exists a natural number which is not greater than 0.


(ii) The negation of the given statement is:


It is false that both the diagonals of a rectangle are equal.


(Or)


There exists at least one rectangle whose both the diagonals are not equal.


(iii) The negation of the given statement is:


It is false that the sum of 4 and 5 is 8.


(Or)


The sum of 4 and 5 is not 8.


(iv) The negation of the given statement is:


It is false that the number 6 is greater than 4.


(Or)


The number 6 is not greater than 4.


(v) The negation of the given statement is:


It is false that every natural number is an integer.


(Or)


Every natural number is not an integer.


(Or)


There exists at least one natural number which is not an integer.


(vi) The negation of the given statement is:


It is false that the number -5 is a rational number.


(Or)


The number -5 is not a rational number.


(vii) The negation of the given statement is:


It is false that all cats scratch.


(Or)


There exists a cat which does not scratch.


(viii) The negation of the given statement is:


It is false that there exists a rational number x such that x2 = 3.


(Or)


There does not exists a rational number x such that x2 = 3


(ix) The negation of the given statement is:


It is false that all students study mathematics at the elementary level.


(Or)


It is not the case that all students study mathematics at the elementary level.


(x) The negation of the given statement is:


It is false that every student has paid the fees.


(Or)


It is not the case that every student has paid the fees.


(Or)


There exists at least a student who does not pay the fees.


(xi) The negation of the given statement is:


It is false that there is some integer k for which 2k = 6.


(Or)


It is not the case there is some integer k for which 2k = 6


(xii) The negation of the given statement is:


It is false that none of the students in this class has passed.


(Or)


It is not the case that none of the students of this class has passed.


More from this chapter

All 18 →
2

Which of the following sentences are statements? In case of a statement, mention whether it is true or false.

(i) Paris is in France.


(ii) Each prime number has exactly two factors.


(iii) The equation x2 + 5|x| + 6 = 0 has no real roots.


(iv) (2 + √3) is a complex number.


(v) Is 6 a positive integer?


(vi) The product of -3 and -2 is -6.


(vii) The angles opposite the equal sides of an isosceles triangle are equal.


(viii) Oh! It is too hot.


(ix) Monika is a beautiful girl.


(x) Every quadratic equation has at least one real root.


 3

Which of the following statements are true and which are false? In each case give a valid reason for your answer.

(i) p: √11 is an irrational number


(ii) q: Circle is a particular case of an ellipse.


(iii) r: Each radius of a circle is a chord of the circle


(iv) S: The center of a circle bisects each chord of the circle


(v) t: If a and b are integers such that a < b, then –a > -b.


(vi) y: The quadratic equation x2 + x + 1 = 0 has no real roots


 1

Split each of the following into simple sentences and determine whether it is true or false.

(i) A line is straight and extends indefinitely in both the directions.


(ii) A point occupies a position, and its location can be determined.


(iii) The sand heats up quickly in the sun and does not cool down fast at night.


(iv) 32 is divisible by 8 and 12.


(v) x = 1 and x = 2 are the roots of the equation x2 – x – 2 = 0.


(vi) 3 is rational, and √3 is irrational.


(vii) All integers are rational numbers, and all rational numbers are not real numbers.


(viii) Lucknow is in Uttar Pradesh, and Kanpur is in Uttarakhand.


 2

Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an ‘inclusive or’ or ‘exclusive or’ is used.

(i) The sum of 3 and 7 is 10 or 11.


(ii) (1 + i) is a real or a complex number.


(iii) Every quadratic equation has one or two real roots.


(iv) You are wet when it rains, or you are in a river.


(v) 24 is a multiple of 5 or 8.


(vi) Every integer is rational or irrational.


(vii) For getting a driving license, you should have a ration card or a passport.


(viii) 100 is a multiple of 6 or 8.


(ix) Square of an integer is positive or negative.


(x) Sun rises or Moon sets.