Applied Mathematics - Mathematical Reasoning

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Description

Mathematical Reasoning

  • Mathematically acceptable statements

  • Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics

  • Validating the statements involving the connecting words difference between contradiction, converse and contrapositive

SUMMARY

1. A mathematically acceptable statement is a sentence which is either true or false.

2. Explained the terms:

– Negation of a statement p: If p denote a statement, then the negation of p is denoted by ∼p.

– Compound statements and their related component statements: A statement is a compound statement if it is made up of two or more smaller statements. The smaller statements are called component statements of the compound statement.

– The role of “And”, “Or”, “There exists” and “For every” in compound statements.

– The meaning of implications “If ”, “only if ”, “ if and only if ”. A sentence with if p, then q can be written in the following ways.

– p implies q (denoted by p ⇒ q)

– p is a sufficient condition for q

– q is a necessary condition for p

– p only if q – ∼q implies ∼p

– The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼p . The converse of a statement p ⇒ q is the statement q ⇒ p. p ⇒ q together with its converse, gives p if and only if q.

3. The following methods are used to check the validity of statements: (i) direct method (ii) contrapositive method (iii) method of contradiction (iv) using a counter example.

What You Will Learn!

  • Introduction
  • Statements
  • New Statements from Old
  • Special Words/Phrases
  • Implications
  • Validating Statements

Who Should Attend!

  • Complete Mathematics for Engineering Entrance Exam Preparation. ( IIT-JEE Main | Advanced | BITSAT | SAT | etc.)
  • Those preparing for board and competitive exams State Board, CBSE, ICSE , IGCSE, MHT-CET & NEET
  • Courses are suitable for 160 countries from Europe, America, Middle East, Asia, Africa and APAC. Notably England, Germany, France, Sweden, Ireland, Scotland, USA, Canada, UAE, Saudi, Qatar, Kuwait, Malaysia, Indonesia, Myanmar, Newzealand, Australia, South Africa, South Korea, Nigeria, Nepal, Sri Lanka, etc