NCERT Solutions for Class 11 Maths Chapter 14

Download NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning गणितीय विवेचन free in PDF. NCERT Solutions for all subjects are available all to download free. These solutions are based on updated NCERT Books for 2018-19 for intermediate students of CBSE, MP Board as well as UP Board.


NCERT Solutions for Class 11 Maths Chapter 14

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Class 11 Maths Chapter 14 Mathematical Reasoning Sols




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
  1. Verify by the method of contradiction that 7 is irrational.
  2. By giving counter example, show that the following statement is false: ‘If n is an odd integer, then n is prime’.
  3. 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’.
  4. Prove by direct method that for any integer ‘n’, n³- n is always even’.


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