# Ex 14.5, 5 - Chapter 14 Class 11 Mathematical Reasoning

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 14.5, 5 Which of the following statements are true and which are false? In each case give a valid reason for saying so. (i) p: Each radius of a circle is a chord of the circle. This statement is false By definition the chord , It should intersect the circle in two points OB & OC are radius of circle But they don’t intersect the circle at two points Hence OB & OC are not the Chord of a circle. Ex14.5, 5 Which of the following statements are true and which are false? In each case give a valid reason for saying so. (ii) q: The centre of a circle bisects each chord of the circle. The given statement is false. Here AB is a chord as it intersect the circle at two points, But it does not pass through center O So, center of circle does not bisect each chord of the circle Ex14.5, 5 Which of the following statements are true and which are false? In each case give a valid reason for saying so. (iii) r: Circle is a particular case of an ellipse. This statement is true Equation of ellipse is 𝑥2𝑎 + 𝑦2𝑏 = 1 Putting a = b 𝑥2 + 𝑦2𝑏 = 1 x2 + y2 = b which is the equation of circle So, circle is particular case of ellipse Ex14.5, 5 Which of the following statements are true and which are false? In each case give a valid reason for saying so. (iv) s: If x and y are integers such that x > y, then –x < –y. x > y Multiplying –1 both sides (–1)x < (–1)y –x < –y This is the rule of inequality Thus, the given statement s is true. Ex14.5, 5 Which of the following statements are true and which are false? In each case give a valid reason for saying so. (v) t: 11 is a rational number. 11 cannot written in the form of 𝑝𝑞 Hence 11 is irrational Hence the given statement is false.

Chapter 14 Class 11 Mathematical Reasoning

Concept wise

- Statements
- Writing negation of statements
- Negation - Checking if true or not
- Finding Compound Statement
- Words 'And' & 'Or'
- Inclusive and exclusive or
- Quantifiers
- Contrapositive and converse
- If then
- If and only if
- Proving not true/false (by giving counter examples)
- Proving True - If and only if
- Proving True - By Contrapositive
- Proving True - By Contradiction
- Necessary and sufficient condition

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.