Relationship of symbols — Abstract Ideas & Symbols Notes for SSC JE Civil

Part 1 of 2

Inequalities & Coded Relations

Last reviewed 22 Sept 2026 · 5 min read

The symbols

A > B (A greater), A < B, A \geq B (greater or equal), A \leq B, A = B

FormulaThe two rules

Rule 1 — the chain must be unbroken. To compare A and D you need a link at every step: $A ? B ? C ? D$ with no gap.

Rule 2 — the arrows must point the same way. $A > B > C$ gives $A > C$ . But $A > B < C$ gives nothing between A and C.

And the strictness rule: a chain of $\geq$ signs gives $\geq$ ; if even one link in the chain is strict ( $>$ ), the result is strict ( $>$ ).

So:

Chain	Conclusion
$A > B > C$	$A > C$
$A \geq B \geq C$	$A \geq C$
$A > B \geq C$	$A > C$
$A \geq B > C$	$A > C$
$A > B < C$	nothing
$A < B > C$	nothing
$A = B \geq C$	$A \geq C$

The either-or case

Two conclusions are an either-or pair when all three of these hold:

they are about the same two terms,
neither follows on its own, and
together they cover every case the chain allows.

The form that almost always appears: the chain proves $A \geq B$ but not which of the two it is. Then " $A > B$ " and " $A = B$ " each fail alone, and together they are certain — so the answer is either I or II follows.

The other legitimate pair is $A > B$ with $A \leq B$ (or $A \geq B$ with $A < B$ ), which exhausts every possibility whatever the chain says.

Coded inequalities

A table defines symbols, for example:

P @ Q means $P \geq Q$
P # Q means $P > Q$
P & Q means $P = Q$
P % Q means $P \leq Q$
P © Q means $P < Q$

Translate every symbol into its inequality first, write the whole chain, then apply the two rules. Never work in the symbols themselves.

Part 2 of 2

Mathematical Operations & Symbol Substitution

Last reviewed 22 Sept 2026 · 5 min read

Substitution questions

A table says, for example: $+$ means $\div$ , $-$ means $\times$ , $\times$ means $+$ , $\div$ means $-$ . Then

18 + 6 - 3 \times 4 \div 2

is read by replacing each symbol first:

18 \div 6 \times 3 + 4 - 2 = 3 \times 3 + 4 - 2 = 11

FormulaThe order that never changes

Substitute the symbols, then apply BODMAS: Brackets, Of, Division and Multiplication (left to right), Addition and Subtraction (left to right). The substitution changes the symbols, never the priority rules.

Interchange questions

Two forms appear:

"If $+$ and $\times$ are interchanged, which equation is correct?" — swap those two symbols wherever they appear in each option and test it.
"Interchange which two signs makes the equation correct?" — try each pair in turn; there are only six pairs among four operators, and usually the first or second works.

A third variant swaps two numbers rather than two signs. Test the options rather than solving in general: it is faster.

Balancing an equation

The question gives an equation with blanks and asks which set of signs fills them, such as $12 ? 4 ? 2 = 10$ . Work backwards from the answer: $12 \div 4 = 3$ gives no 10; $12 - 4 + 2 = 10$ ✓. Test option by option, and remember BODMAS applies to your filled-in version too.

Defined operations

A rule defines a new operator: $a * b = a^{2} - b$ , or $a Δ b = \frac{a + b}{2}$ . Substitute the numbers into the definition exactly as written, taking care with the order — most defined operations are not symmetric, so $a * b \neq = b * a$ .

For nested expressions, evaluate the innermost bracket first: $(3 * 2) * 4$ means find $3 * 2$ , then apply $*$ with 4.

Inserting symbols

"Insert arithmetic signs to make $6_3_2 = 4$ true." Try division first (it constrains most), then multiplication: $6 \div 3 + 2 = 4$ ✓.

Worked examples

Worked ExampleExample 1 — plain substitution

If $+$ means $\times$ , $-$ means $+$ , $\times$ means $\div$ and $\div$ means $-$ , find $16 + 4 \div 2 - 8 \times 4$ .

Solution. Substituting: $16 \times 4 - 2 + 8 \div 4 = 64 - 2 + 2 =$ 64.

Worked ExampleExample 2 — BODMAS after substitution

If $\times$ means $+$ and $+$ means $\div$ , find $12 \times 6 + 3$ .

Solution. $12 + 6 \div 3 = 12 + 2 =$ 14 — division is done before addition even though it was written second.

Worked ExampleExample 3 — which equation is correct

If $+$ and $\div$ are interchanged, which is correct? (a) $16 \div 4 + 2 = 10$ (b) $18 + 3 \div 6 = 12$

Solution. Swapping the two symbols in (a): $16 + 4 \div 2 = 18 \neq = 10$ . In (b): $18 \div 3 + 6 = 12$ ✓ → (b).

Worked ExampleExample 4 — which signs to interchange

Which two signs should be interchanged to make $9 + 3 - 4 \times 2 = 19$ correct?

Solution. As printed the left side is $9 + 3 - 8 = 4$ . Test the pairs:

$+$ and $\times$ : $9 \times 3 - 4 + 2 = 25$ ✗
$+$ and $-$ : $9 - 3 + 4 \times 2 = 14$ ✗
$-$ and $\times$ : $9 + 3 \times 4 - 2 = 19$ ✓

So $-$ and $\times$ are interchanged. With only three pairs to try among three signs, testing is quicker than reasoning.

Worked ExampleExample 5 — a defined operation

If $a * b = a^{2} - b$ , find $5 * 3$ and $3 * 5$ .

Solution. $5 * 3 = 25 - 3 =$ 22; $3 * 5 = 9 - 5 =$ 4. The operation is not symmetric.

Worked ExampleExample 6 — a nested defined operation

With $a Δ b = \frac{a + b}{2}$ , find $(8Δ4) Δ6$ .

Solution. $8Δ4 = 6$ ; then $6Δ6 =$ 6.

Worked ExampleExample 7 — inserting signs

Insert signs to make $9_3_2 = 5$ true.

Solution. $9 \div 3 + 2 =$ 5 ✓.

Worked ExampleExample 8 — interchanging numbers

Which two numbers should be interchanged to make $8 + 6 \times 4 - 2 = 30$ correct?

Solution. As printed: $8 + 24 - 2 = 30$ ✓ — the equation is already correct, so no interchange is needed. Check the given equation before hunting for a swap.

Worked ExampleExample 9 — mixed symbols

If $A$ means $+$ , $B$ means $-$ , $C$ means $\times$ and $D$ means $\div$ , find $15 A 12 D 4 C 3 B 6$ .

Solution. $15 + 12 \div 4 \times 3 - 6 = 15 + 9 - 6 =$ 18.

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Inequalities & Coded Relations

The symbols

The either-or case

Coded inequalities

Mathematical Operations & Symbol Substitution

Substitution questions

Interchange questions

Balancing an equation

Defined operations

Inserting symbols

Worked examples

Finished reading? Test yourself.