Syllogism for LIC AAO

Syllogism questions are short, and once the method is steady they take about 30 seconds each. That makes them some of the cheapest marks in the prelims Reasoning section. They are also easy to lose: a conclusion can sound true, even be true in real life, and still not follow from the statements. The whole skill is to test each conclusion against every picture the statements allow, not just the first one you draw.

Statement types

These conversions always hold:

• "Some A are B" gives "Some B are A".
• "All A are B" gives "Some A are B" and "Some B are A".
• "No A is B" gives "No B is A".

"All A are B" does not give "All B are A".

The method

1. Draw the minimum diagram. Show only what the statements force. Do not add overlaps that are not stated.
2. Test a definite conclusion ("Some A are C", "No A is C"): it follows only if it holds in every diagram the statements allow. Try to break it by redrawing. If you can break it, it does not follow.
3. Test a possibility conclusion ("All A being C is a possibility"): it follows if you can draw at least one diagram where it is true without breaking any statement.
4. Check for either–or. If neither of two conclusions follows, but they are about the same two terms and together cover every case, the answer is "either I or II follows".

The pairs that form either–or are "Some A are B" with "No A is B", and "All A are B" with "Some A are not B". Each pair covers every possibility between two terms, so one of the two must be true.

Worked examples

Example 1

Statements: All policies are contracts. Some contracts are agreements.

Conclusions: I. Some policies are agreements. II. Some agreements are contracts.

• The agreements may overlap only the part of contracts that is not policies. So I can be broken. ✗
• "Some contracts are agreements" turns round to "Some agreements are contracts". ✓
• Only II follows.

Example 2

Statements: No claim is a premium. All premiums are payments.

Conclusions: I. Some payments are not claims. II. No claim is a payment.

• Every premium is a payment and no premium is a claim. Those payments are not claims. ✓
• Claims may still overlap payments that are not premiums, so II can be broken. ✗
• Only I follows.

Example 3

Statements: Only a few agents are advisers. All advisers are experts.

Conclusions: I. Some agents are experts. II. All agents are advisers. III. All agents being experts is a possibility.

• The agents who are advisers are experts. ✓
• "Only a few" means some agents are not advisers, so II is false. ✗
• The agents who are not advisers can still sit inside experts. Nothing forbids it. ✓
• I and III follow.

Example 4

Statements: Some risks are losses. No loss is a gain.

Conclusions: I. Some risks are not gains. II. All risks being gains is a possibility.

• The risks that are losses cannot be gains. ✓
• If all risks were gains, those risk-losses would be gains, which breaks the second statement. ✗
• Only I follows.

Example 5

Statements: All funds are schemes. Some schemes are bonds.

Conclusions: I. Some funds are bonds. II. No fund is a bond.

• Bonds may or may not reach the funds inside schemes. Neither conclusion is certain.
• Both are about funds and bonds, and one of "some are" or "none are" must be true.
• Either I or II follows.

Practice set

1. Some risks are losses. All losses are costs. I. Some risks are costs. II. All costs being risks is a possibility.
2. All agents are employees. No employee is a customer. I. No agent is a customer. II. Some customers are agents.
3. Some premiums are fees. Some fees are charges. I. Some premiums are charges. II. No premium is a charge.
4. Only a few banks are insurers. No insurer is a broker. I. Some banks are not brokers. II. All banks being brokers is a possibility.
5. All claims are documents. All documents are files. I. All claims are files. II. Some files are claims.
6. No bond is a share. Some shares are units. I. Some units are not bonds. II. Some bonds are units.
7. Some policies are plans. All plans are products. No product is a loan. I. Some policies are not loans. II. Some plans are loans.
8. All nominees are members. Only a few members are voters. I. Some nominees are voters. II. All nominees being voters is a possibility.

Answers

1. Both follow. The risks that are losses are costs. Costs can sit entirely inside risks without breaking either statement.
2. Only I follows. Agents lie inside employees, which never touch customers. II contradicts I.
3. Either I or II follows. The two "some" statements give no link between premiums and charges, and I and II together cover every case.
4. Only I follows. The banks that are insurers cannot be brokers. For the same reason, all banks cannot be brokers.
5. Both follow. Claims sit inside documents, which sit inside files. So all claims are files, and some files are claims.
6. Only I follows. The units that are shares cannot be bonds. Bonds and units may or may not overlap, so II is not certain.
7. Only I follows. The policies that are plans are products, and no product is a loan. Plans are products, so no plan can be a loan.
8. Only II follows. Nominees might all sit in the non-voter part of members, so I is not certain. They might equally all sit in the voter part, so II is possible.

A quick checklist for the exam

• Draw first, read conclusions second.
• For "only a few", draw both parts: the some-are and the some-are-not.
• Before marking "does not follow", try one more diagram.
• Before marking "follows", try to break it.
• Check every pair of failed conclusions for either–or.

What to do next

• Do ten syllogisms daily for a week, writing "definite" or "possibility" beside each conclusion before you test it.
• Pair this topic with inequalities; both are rule-based and quick.
• Add syllogism to your daily quick set in the reasoning plan.