The four standard statements

Syllogism questions use four statement forms. All A are B places the whole of A inside B. No A is B keeps the two classes completely apart. Some A are B means at least one A is B; it does not imply that some A are not B, and it allows the possibility that all A are B. Some A are not B means at least one A lies outside B. Most errors come from reading these statements with everyday meaning rather than logical meaning.

Conversion: reversing a statement

All A are B converts only to Some B are A, because B may be larger than A. No A is B converts fully to No B is A. Some A are B converts to Some B are A. Some A are not B has no valid conversion: from Some animals are not dogs nothing follows about dogs being animals or not. Conversions often supply the conclusion directly, so check them before combining premises.

Combining two premises

A definite conclusion links the two end terms through the shared middle term. The standard pairings are:

• All A are B + All B are C → All A are C
• All A are B + No B is C → No A is C
• Some A are B + All B are C → Some A are C
• Some A are B + No B is C → Some A are not C
• No A is B + All B are C → Some C are not A (not Some A are not C)
• No A is B + Some B are C → Some C are not A
• All A are B + Some B are C → no definite conclusion between A and C (the middle term B is never taken as a whole)

Two particular premises give no definite conclusion, and neither do two negative premises. If one premise is particular, any conclusion is particular; if one is negative, the conclusion is negative.

Possibility conclusions

A conclusion phrased as a possibility, such as All A being C is a possibility, follows whenever no definite relation rules it out, i.e. whenever at least one valid diagram shows it. It fails only when a definite conclusion contradicts it. If No A is C is established, then Some A being C is not a possibility. If Some A are not C is established, then All A being C is not a possibility. Draw the minimum Venn diagram first, then ask whether the proposed case can be drawn without breaking any statement.

Complementary pairs: either I or II

When neither conclusion follows on its own, check whether the two form a complementary pair. Both must have the same subject and predicate, one must be affirmative and the other negative, and together they must exhaust all cases. The pairs are Some A are B with No A is B, and All A are B with Some A are not B. Because both Some and No convert, the Some + No pair still qualifies when subject and predicate are swapped (Some A are B with No B is A). Some A are B with Some A are not B is not a pair, because both can be true together. If the pair qualifies and neither member is definite, the answer is “either I or II follows”. If one member is already definite, the either-or option does not apply.

Data sufficiency: the order of testing

Data sufficiency asks whether the statements fix a unique answer, not what the answer is. The usual answer options are: I alone is sufficient; II alone is sufficient; either I alone or II alone is sufficient; both together are needed; neither is sufficient even together. Test the statements in this order:

1. Test Statement I with the question stem alone, ignoring II.
2. Then test II alone, setting I aside.
3. Combine them only if neither works independently.

If each works alone, the answer is “either statement alone”, not “both together”. If even the combination leaves more than one possible answer, the data is insufficient. Use only the stem and the statements: do not assume gender from a name, a starting direction, or that numbers are integers unless stated.

Data sufficiency: uniqueness and impossible cases

In a class of 40, P is 15th from the bottom, so P is 40 − 15 + 1 = 26th from the top. Suppose instead Q is 10th from the top with exactly 15 students between Q and P. If P is below Q, P is 10 + 15 + 1 = 26th. Placing P above Q would need at least 16 students above Q (the 15 in between plus P), but only 9 exist. One branch is impossible, so the answer is unique. Before declaring a statement insufficient because it seems to allow two cases, check whether each case can actually exist. Equally, small changes to the stem, such as removing the class strength, can turn a sufficient statement into an insufficient one.

Key points to remember

Frequently asked questions

How is “All A are B” converted in syllogisms?

Only to “Some B are A”, because B may be larger than A. “No A is B” converts fully to “No B is A”, “Some A are B” to “Some B are A”, and “Some A are not B” has no valid conversion.

What does No A is B plus All B are C give?

Some C are not A. The B portion of C cannot be A. Nothing definite follows about A with respect to C, so “Some A are not C” does not follow.

When is the answer “either I or II follows”?

When neither conclusion is definite, both have the same subject and predicate, and they form a complementary pair: Some + No, or All + Some not. Some + Some not is not a complementary pair.

When does a possibility conclusion follow?

When at least one valid diagram shows it, i.e. no definite conclusion contradicts it. If No A is C is definite, Some A being C is not a possibility.

What is the order of testing in data sufficiency?

Test Statement I alone, then Statement II alone, and combine them only if neither is sufficient by itself. If each works alone, the answer is “either statement alone”.

Practice: 10 MCQs

Attempt all ten questions, then press Submit. The correct answer and a short explanation appear under every question, followed by your score analysis.

Verification notes

• Each conversion, pairing and MCQ was checked against classical categorical logic (A/E/I/O propositions; valid moods such as Barbara, Celarent, Darii, Ferio; conversion and distribution rules) and the conventions of Indian competitive exams for possibility and either-or questions.
• The rank cases were recomputed: 40 − 15 + 1 = 26; 10 + 15 + 1 = 26; the upward branch needs at least 16 students above Q, but only 9 exist.