A deductive argument is one whose premises are meant to guarantee its conclusion. For example: “Every contract over £50,000 must be reviewed by legal. The Harland contract is worth £64,000. Therefore the Harland contract must be reviewed by legal.” If the premises are true and the argument is valid, the conclusion cannot be false.
Deductive arguments are what deductive reasoning tests are made of. You are given the premises and asked whether a conclusion follows, which you can try in a free deductive reasoning test.
Deductive argument definition
An argument is a set of statements, called premises, offered as reasons for another statement, the conclusion. In a deductive argument the claim is a strong one: the premises are supposed to make the conclusion certain, not just likely.
That sets it apart from an inductive argument, where the premises only make the conclusion probable. “Every contract over £50,000 we have checked went through legal, so this one probably did” is inductive. It could be wrong even if every premise is true. A valid deductive argument cannot be.
The parts of a deductive argument
- Premises. The starting statements, usually general rules or facts, such as “every contract over £50,000 must be reviewed by legal”.
- An indicator. A word or phrase that signals the conclusion, such as “therefore”, “so”, “it follows that” or “must”.
- The conclusion. The statement the premises are said to force, such as “the Harland contract must be reviewed by legal”.
Arguments in tests are not always written in this order. The conclusion can come first (“The Harland contract needs legal review, because…”). Finding the conclusion before you judge the argument saves confusion.
Valid and invalid deductive arguments
A deductive argument is valid when it is impossible for all the premises to be true and the conclusion false. Validity is about structure, not about whether the statements are true.
Valid. All senior consultants hold a professional qualification. Dev is a senior consultant. So Dev holds a professional qualification.
Invalid. All senior consultants hold a professional qualification. Dev holds a professional qualification. So Dev is a senior consultant.
The second argument fails because the first premise works in one direction only. It tells you every senior consultant is qualified. It does not tell you every qualified person is a senior consultant. Dev could be a qualified junior consultant.
Sound and unsound deductive arguments
A deductive argument is sound when it is valid and all of its premises are true. Only a sound argument proves its conclusion.
Valid but unsound. All of our offices are in Scotland. Our Cardiff branch is one of our offices. So our Cardiff branch is in Scotland. The structure is perfect. The conclusion is false because the first premise is false.
Valid and sound. Every employee must complete data protection training each year. Maria is an employee. So Maria must complete data protection training this year. If both premises are true, so is the conclusion.
In an aptitude test you are almost always asked about validity only. The instructions tell you to treat the premises as true, however unlikely they sound, and to judge whether the conclusion follows from them.
Examples of deductive arguments by form
Valid deductive arguments tend to follow a handful of standard forms. Each one below always works, whatever you put into it.
Categorical syllogism. All members of the audit team have read-only access. Some new starters are members of the audit team. So some new starters have read-only access.
Modus ponens (if P then Q; P; so Q). If the client signs by Friday, the project starts on Monday. The client signed on Thursday. So the project starts on Monday.
Modus tollens (if P then Q; not Q; so not P). If the payment had cleared, the account would show a zero balance. The account does not show a zero balance. So the payment has not cleared.
Chain argument (if P then Q; if Q then R; so if P then R). If the launch slips, the campaign is delayed. If the campaign is delayed, the quarterly target is at risk. So if the launch slips, the quarterly target is at risk.
Disjunctive argument (P or Q; not P; so Q). The missing file is on the shared drive or in the archive. It is not on the shared drive. So it is in the archive.
You will find these forms used in test-style questions in these deductive reasoning examples.
Invalid arguments that look deductive
Some arguments borrow the shape of a valid form but break it. The two most common both misuse an if-then rule.
- Affirming the consequent. If the payment had cleared, the balance would be zero. The balance is zero. So the payment has cleared. Invalid, because the balance could be zero for another reason, such as a refund.
- Denying the antecedent. If the client signs by Friday, the project starts on Monday. The client did not sign by Friday. So the project does not start on Monday. Invalid, because the rule says nothing about what happens if the client signs later. The project might start on Monday anyway.
A third common error is reversing an “all” statement, as in the Dev example above. “All A are B” never gives you “all B are A”.
How to check any deductive argument
The most reliable test for validity is to look for a counterexample. Ask: can I imagine a situation where every premise is true and the conclusion is false?
- If you can, the argument is invalid.
- If you genuinely cannot, it is valid.
Try it on the invalid Dev argument. Imagine a firm where every senior consultant is qualified, and Dev is a qualified analyst. Both premises are true, and the conclusion “Dev is a senior consultant” is false. So the argument is invalid.
Now try it on the audit team syllogism. If all audit team members have read-only access, and some new starters are in the audit team, those particular new starters must have read-only access. There is no way to make the premises true and the conclusion false. So the argument is valid.
Drawing the groups as overlapping circles helps with “all” and “some” statements. The counterexample check works for every type.
Deductive arguments in aptitude tests
Deductive reasoning tests present arguments like these and ask you to judge them. You might choose the conclusion that follows, decide whether a conclusion is true, false or cannot be determined, or spot the invalid step. The skills are the ones on this page: accept the premises, know the valid forms, watch for the reversed rule, and look for a counterexample when you are unsure.
For the wider picture, read what deductive reasoning is, and for practical advice on timing and traps see how to pass a deductive reasoning test. Then put it into practice with a timed deductive reasoning practice test.
