RS Aggarwal Solution Class 11 Maths Chapter 29 - Mathematical ReasoningShare
RS Aggarwal Solution Class 11 Maths Chapter 29 - Mathematical Reasoning
Which of the following sentences are statements? In case of a statement mention whether it is true or false.
(i) The sun is a star.
(ii) √7 is an irrational number.
(iii) The sum of 5 and 6 is less than 10.
(iv) Go to your class.
(v) Ice is always cold.
(vi) Have you ever seen the Red Fort?
(vii) Every relation is a function.
(viii) The sum of any two sides of a triangle is always greater than the third side.
(ix) May God bless you!
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.
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
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.