Logical Reasoning: Deduction, Inference, and the Art of Spotting Bad Arguments

From the first premise, every electrician is a trained person.

From the second premise, some trained people are licensed.

This does NOT mean that the licensed trained people include any electricians. The licensed people could be non-electrician trained people (like plumbers, nurses, or welders who are also trained).

Option A (All electricians are licensed) is not supported, because the premise says only "some" trained people are licensed.

Option B (Some electricians are licensed) is tempting but invalid. The "some trained people" could be entirely non-electricians.

Option C (No electricians are licensed) is also unsupported.

Only option D is correct: we cannot conclude anything about electricians and licensing from these premises.

This is a classic syllogism trap. "Some" is not transitive through "all."

The statement is "If rain, then cancelled." This is If A, then B.

We are told B is false: the match was NOT cancelled.

By modus tollens (if B is false then A must be false), we can conclude A is false: it did not rain.

If it had rained, the match would have been cancelled (per the rule). Since it was not cancelled, rain cannot have happened.

Option A is the wrong direction (affirming the consequent).

Option D is the common trap: candidates hedge when the answer is actually certain. Modus tollens is a valid deduction.

Step 1: Dan is at position 1. So Dan = 1.

Step 2: Ann is not at position 1 or 5. So Ann is in {2, 3, 4}.

Step 3: Bob is immediately left of Carla. So Bob-Carla form a pair like (2,3), (3,4), or (4,5).

Step 4: Try Bob=2, Carla=3. Then Ann must be in {4}. Evan gets position 5. Check: all constraints satisfied.

Step 5: Verify other configurations. Bob=3, Carla=4. Then Ann must be in {2}. Evan gets position 5. Also works.

Step 6: Try Bob=4, Carla=5. Then Ann is in {2, 3}. Evan takes the other of 2 or 3. Both would give Evan at position 2 or 3, not 5.

Step 7: Two of three configurations give Evan=5, one gives Evan at 2 or 3.

Reconsider carefully. Actually, in the third case, Evan is NOT at position 5, Carla is. But the question asks what position Evan MUST be in. If multiple configurations are consistent, Evan is not uniquely determined.

The trap: the question asks what Evan MUST be. Since Evan could be 2, 3, or 5 depending on arrangement, no position is forced. This is a trick question.

Actually let me re-verify configuration 3: Bob=4, Carla=5, Dan=1, Ann in {2,3}. Evan takes the remaining spot from {2,3}. Evan could be 2 or 3. So Evan is NOT uniquely position 5.

The intended answer depends on whether configurations 1 and 2 (Evan=5) are forced. Since configuration 3 (Evan at 2 or 3) is also valid, there is no unique answer and the question would be flawed in real test scoring.

For the purposes of this worked example, if we assume the test-writer intended the constraint "Ann must be interior" to force Bob-Carla to positions (2,3) or (3,4), the unique Evan position becomes 5 (since positions 2, 3, 4 are filled by Ann, Bob, Carla). The worked solution shows the method: systematically test each placement.