Crossover Aptitude Test Logical Reasoning: Syllogisms 4

Question 1

Premise 1: All squares are rectangles. Premise 2: All rectangles are parallelograms. What follows?

Accepted Answer

All squares are parallelograms.

Answer

By the transitive property of universal affirmatives, all squares must be parallelograms.

Question 2

No X is Y. All Z are Y. Which is a valid conclusion?

Accepted Answer

No Z is X.

Answer

Since Z is entirely within Y and X has no overlap with Y, Z and X cannot overlap at all.

Question 3

Some students pass exams. All who pass exams get certificates. Which is certain?

Accepted Answer

Some students get certificates.

Answer

The students who pass exams must get certificates, so some students definitely get certificates.

Question 4

All birds have wings. Penguins are birds. Penguins cannot fly. What can be concluded?

Accepted Answer

Penguins have wings but cannot fly.

Answer

All birds have wings so penguins have wings, and the given fact states penguins cannot fly — both are true simultaneously.

Question 5

Some politicians are honest. All honest people are trustworthy. Which is DEFINITELY true?

Accepted Answer

Some politicians are trustworthy.

Answer

The honest politicians are also trustworthy, so at least some politicians are trustworthy.

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