Pay attention to the implications of each premise. What can you conclude from each of them? Is this used correctly in the conclusion?
Flawed, see solution.
Practice makes perfect
Let's start by identifying the premises and the conclusion in the given syllogism.
Premise: No trapezoids are rectangles.
Premise: Some rectangles are not squares.
Conclusion: Some squares are not trapezoids.
We will analyze the premises and the conclusion separately.
Premises
The first premise states that no trapezoid is a rectangle, which implies that no rectangle is a trapezoid either. This is true, and we can verify this by taking a look at the definition of trapezoid.
Trapezoid: A quadrilateral with exactly one pair of parallel sides.
Since rectangles have two parallel sides, we can confirm that no rectangle is a trapezoid.
The second premise tell us that some rectangles are not squares, this is true. However, notice that all squares are rectangles, and not just some of them.
Conclusion
Having analyzed and discussed the implications of each premise, we can see that the conclusion uses the information of the second premise incorrectly.
In the conclusion it is assumed that if some rectangles are not squares, then some squares are not rectangles.
Conclusion: Some squares are not trapezoids.
Since the conclusion has an incorrect use of the second premise, the deductive reasoning is flawed. We could have also noticed this by realizing that no square is a trapezoid. However, keep in mind that we are analyzing the correctness of the deductive reasoning, not just the veracity of the premises or the conclusion.
