Mathematical Reasoning Notes for IIT JEE, Download PDF!
JEE Main Short Notes
Mathematical reasoning is one of those topics which is easy to score and it assures you of at least one question in the JEE Main question paper. So, revise this topic and assure guaranteed 4 marks in your JEE Main examination. This topic is exclusively part of JEE Main, BITSAT and some other engineering entrance examination.
Mathematical reasoning is of two kinds:
A) Inductive Reasoning
B) Deductive Reasoning
** The link to download Mathematical Reasoning notes for IIT JEE preparation at the end of the post.
1. MATHEMATICAL INDUCTION
The word ‘induction’ means to generalize a statement from some given cases (facts).
The Principle of Mathematical Induction is a technique to establish the truth of a given mathematical statement which has been formulated in terms of the natural number ‘n’.
Assume that the statement is P(n) which has an association with some positive integer ‘n’.
(a) Step 1 involves an examination of the statement for n=1.
(b) In Step 2 it is assumed that the statement is true for a positive integer ‘k’.
(c) In Step 3, the truth of P(k+1) is established.
2. DEDUCTIVE REASONING
Any sentence is an acceptable mathematical statement if it is either a true statement or a false statement, but it cannot be both. It is generally denoted as an alphabet followed by a colon and then the statement.
2.2 Compound statement
A combination of multiple mathematical statements connected through some logical
2.3 Negation of a statement
If any statement is denied being true, then that it is the negation of the statement.
If a statement is denoted by ‘p’ then its negation is denoted by '∼ p'.
3 LOGICAL OPERATIONS
The compound statements are connected by some logical operations. These logical operations are denoted by some special words/phrases, also called as connectives.
3.1 ‘And’ Operation
If each of the component statement in a compound statement is ‘true’ then the compound statement is ‘true’.Even if any one of the component statements using is ‘false’, the compound statement is ‘false’.It is denoted by ‘ v ’.
3.2 ‘Or’ Operation
If anyone (or more than one) component statements of a compound statement is/are true, then the compound statement is ‘true’.The compound statement using ‘or’ is ‘false’ only if all the component statements are false. It is denoted by ’ ^ ‘
A compound statement ‘a’ implies ‘b’ means that the statement ‘a’ is enough condition for statement ‘b’ and vice-versa. It is denoted as p ⇒ q.
4 Types of statements
A compound statement is a tautology if and only if it is always a ‘true’ statement.
A compound statement is a fallacy if and only if it is always a ‘false’ statement.
A statement ‘p’ is a contradiction to another statement ‘q’ if the q = ∼ p.
If a compound statement is “if ‘p’ then ‘q’’’, the converse of the statement is “if ‘q’ then ‘p’ ’’. It is denoted as if p ⇒ q then q ⇒ p
If a compound statement is “if ‘p’ then ‘q’ ’’, the contrapositive of the statement is “if ‘not p’ then ‘q’ ’’ .It is denoted as if p ⇒ q then ∼p ⇒ q
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