# Example, 8 - Chapter 14 Class 11 Mathematical Reasoning

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example, 8 Identify the type of “Or” used in the following statements and check whether the statements are true or false: (i)2 is a rational number or an irrational number. The component statements are p: 2 is a rational number. q: 2 is an irrational number. We know that 2 is irrational number as it cant be Written in form 𝑝𝑞 Hence first statement is false and second statement is true Since the connecting world to ‘Or’ So the compound statement is true It is exclusive or as 2 is either rational or not It cant be both. Example, 8 Identify the type of “Or” used in the following statements and check whether the statements are true or false: (ii) To enter into a public library children need an identity card from the school or a letter from the school authorities. The component statements are p: To get into a public library children need an identity card. q: To get into a public library children need a letter from the school authorities. Children can enter the library it they have an identity card or the letter, as well as both. Hence, ‘Or’ is inclusive. Both p & q statements are true. & the connecting word is ‘Or’ Hence component statement are true Example, 8 Identify the type of “Or” used in the following statements and check whether the statements are true or false: (iii) A rectangle is a quadrilateral or a 5-sided polygon. The component statement are: p : A Rectangle is a quadrilateral. q : A Rectangle is a 5–sided polygon. A rectangle can be quadrilateral . But cannot be 5 – sided polygon. Hence ‘or’ is exclusive. We know that a rectangle is a quadrilateral . Hence p is true. A rectangle can not be 5 - sided polygon as it has 4 sides Hence q is false. The connecting word is ‘Or’ Hence compound statement is true.

Inclusive and exclusive or

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.