Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 2 — Questions and Answers
Question 1: All squares are rectangles. All rectangles are parallelograms. Which conclusion is VALID?
- All squares are parallelograms (Correct answer)
- All parallelograms are squares
- No squares are parallelograms
- Some rectangles are not squares
Correct answer: All squares are parallelograms
Barbara (AAA-1): All S→R, All R→P, therefore All S→P.
Question 2: Some birds cannot fly. All penguins are birds. Which conclusion is DEFINITELY valid?
- All penguins are birds (Correct answer)
- Some penguins cannot fly
- All birds cannot fly
- Some birds can fly
Correct answer: All penguins are birds
The only statement that necessarily follows from the given premises is the second premise itself: all penguins are birds.
Question 3: No vegetarians eat meat. Jane is a vegetarian. Therefore:
- Jane does not eat meat (Correct answer)
- Jane sometimes eats meat
- Some vegetarians eat meat
- Jane eats only vegetables
Correct answer: Jane does not eat meat
Jane ∈ vegetarians, and no vegetarian eats meat → Jane does not eat meat.
Question 4: All politicians are public speakers. Some liars are politicians. Which conclusion follows?
- Some liars are public speakers (Correct answer)
- All public speakers are liars
- No liars are public speakers
- All liars are politicians
Correct answer: Some liars are public speakers
The liar-politicians are public speakers (all politicians are public speakers) → some liars are public speakers.
Question 5: Premise 1: If it rains, the ground gets wet. Premise 2: The ground is wet. What can we conclude?
- It rained
- It may or may not have rained (Correct answer)
- It did not rain
- The ground is always wet
Correct answer: It may or may not have rained
Affirming the consequent is a fallacy — wet ground could have other causes; we cannot conclude it rained.
Question 6: All A are B. No B are C. Which conclusion is VALID?
- No A are C (Correct answer)
- Some A are C
- All C are A
- Some B are A
Correct answer: No A are C
EAE-2 (Cesare): All A→B; No B→C; therefore No A→C.
Question 7: Some cats are black. Some black things are cars. Which conclusion MUST follow?
- Some cats are cars
- No cats are cars
- Some black cats are cars
- Nothing must follow (Correct answer)
Correct answer: Nothing must follow
Two particular premises (II) yield no valid syllogistic conclusion — the overlap of 'cats∩black' and 'black∩cars' may not intersect.
Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 2
All squares are rectangles.
All rectangles are parallelograms.
Which conclusion is VALID?