IEMJEE Maths preparation: Union of two sets — error clinic and diagnostic check

The error pattern

Adding the two group sizes without subtracting their intersection double-counts shared members.

An error clinic starts with the reason an approach fails, rather than memorising an exception in isolation. State the hidden assumption or changed definition that makes the mistaken approach tempting.

Rebuild the correct model

The union contains every element belonging to at least one of the two sets. An element in both sets must appear only once.

n(A∪B)=n(A)+n(B)−n(A∩B) for finite sets.

Write the domain, any nonzero-denominator conditions and the exact quantity requested. A correct algebraic manipulation must still respect those restrictions. Exact fractions and symbols are preferable until a decimal approximation is specifically useful.

Diagnostic question

Of 40 applicants, 22 study mathematics, 17 study computing and 8 study both. How many study neither?

Before solving, write one sentence explaining how the error pattern above could affect this question. Then choose a method that keeps the correct definition, convention or model visible.

Diagnostic answer

The union is 22+17−8=31, so 40−31=9 study neither.

Compare the actual reasoning steps, not only the final value or chosen word. A correct final result obtained from inconsistent assumptions is not a dependable method for a different problem.

Verification checklist

Substitute a candidate result into the original statement where possible. Inspect sign, endpoint inclusion and whether a real or complex answer is requested. The simplified expression and the original expression can have different domains even when their nearby values agree.

Keep an error-log entry with the topic, the failed step, the corrected principle and a later reattempt. Track whether the same failure recurs. The purpose is to improve reasoning on this topic; the log is not a certificate of examination performance.

Official sources and verification

Sources checked on 26 October 2026. A source’s date, programme and campus limit which claims it supports. Official pages may change after review.

1. UEM — IEMJEE examination information

   Historical examination pattern; verify the current cycle on the central portal.

2. NTA — explicitly labelled JEE Main 2026 syllabus

   Historical PCM syllabus reference. Lessons and exercises are independently authored, not official IEMJEE papers or verified 2027 paper predictions.

3. NCERT — official textbook catalogue

   Primary textbook reference for checking school-level concepts. This directory does not certify the independent lesson or establish IEM examination weightage.

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