## Mathematical Operations

Category : 9th Class

Type-I

Solving by Substitution

In this type of problems, you are required to simplify the given statement by substituting various signs and numerals as per given terms. To simplify a statement, the BODMAS rule is very useful.

Type-II

Interchanging of Signs and Numbers

In this type of problems, you would require to interchange the pair(s) of symbols/numbers. Simplify if asked the given statement(s) using BODMAS rule.

Type-III

Analysing the Conclusions

In this type of problems, relations between different statements are given in terms of mathematical operations (less than, more than etc.) A student is required to analyse amongst them to get correct conclusions.

EXAMPLE

Consider the following statements.

'A @ B' means 'A is not greater than B'.

'A © B' means 'A is not smaller than B'.

'A # B' means "A is neither greater than nor equal to B'.

'A $B' means "A is neither smaller than nor equal to B'. Assuming the given below statements to be true, analyse which of the two conclusions I and II is/are definitely true and choose your option accordingly. Statements: P @ Q, Q © R, R # S. Conclusions: 1. P$ R        II. R $P (a) Only I is true (b) Only II is true (c) None is true (d) Both are true Explanation (c): We have A@B AB A < B A©B A B A > B A # B A B and A B A < B A$ B A  B and A  B  A > B

Given statements: P < Q, Q >. R, R < S.

Relationship between P and R: P < Q, Q >. R

No definite relationship between P and R.

Hence none of I and II is true.

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