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## NCERT Solutions for Class 11 Maths Chapter 14

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### Class 11 Maths Chapter 14 Mathematical Reasoning Sols

**Download Exercise 14.1****Download Exercise 14.2****Download Exercise 14.3****Download Exercise 14.4****Download Exercise 14.5****Download Miscellaneous Exercise 14****NCERT Books for Class 11****Revision Books for Class 11**- Hindi Medium Solutions will be uploaded very soon.

#### Important Terms on Mathematical Reasoning

- A sentence is called a
*statement*if it is either true or false but not both simultaneously. - The denial of a statement p is called its negation and is written as ~p and read as not p.
- Compound statement is made up of two or more simple statements. These simple statements are called
*component statements*. - ‘And’, ‘or’, ‘If–then, ‘only if’, ‘If and only if’ etc. are connecting words, which are used to form a compound statement.
- Two simple statements p and q connected by the word ‘and’ namely ‘p and q’ is called a conjunction of p and q and is written as p^q.

- Two simple statements p and q connected by the word ‘or’ the resulting compound statement ‘p or q’ is called
*disjunction*of p and q and is written as pvq. - If in a compound statement containing the connective ‘or’ all the alternatives cannot occur simultaneously, then the connecting word ‘or’ is called as exclusive ‘or’.
- If, in a compound statement containing the connective ‘or’, all the alternative can occur simultaneously, then the connecting word ‘or’ is called as inclusive ‘or’.

##### Important Extra Questions on Mathematical Reasoning

- Verify by the method of contradiction that 7 is irrational.
- By giving counter example, show that the following statement is false: ‘If n is an odd integer, then n is prime’.
- Show that the following statement is true by method of contra positive: ‘If x is an integer and x² is even, then x is also even’.
- Prove by direct method that for any integer ‘n’, n³- n is always even’.