Question

If all squares are rectangles, and if all rectangles are parallelograms, then all squares are parallelograms. Which law of property does this example illustrate? Substitution property
Symmetric property
Law of Syllogism
Law of Detachment

Answer 1

That's the Law of Syllogism

Let's go through the list.

Substitution property

This is a very general rule in math that allows us to substitute things that are equal for one another.

Symmetric property

Abstractly, a relation is a set of ordered pairs. A relation R is symmetric when

$(a,b) \in R \iff (b,a) \in R$

Usually we talk about equality or congruence being symmetric: a=b implies b=a.

Law of Syllogism

That's a rule of logic that says if a implies b and b implies c then a implies c. Again it's a very general rule that applies across all mathematics.

Law of Detachment

This one is more commonly known as modus ponens. It's a general rule of formal logic, applying across all mathematics.

If we know two propositions p implies q and p then we can conclude a third proposition, q.

Formal logic acts at a purely syntactic level. It is a mechanistic pushing around of symbols on the page. Nonetheless, in the real world when the premises of an argument are true, the conclusions drawn as a result of formal logic will be true as well.

Answer: Law of Syllogism