What is the Law of Syllogism and the Law of Detachment?

see below.

The Law of Detachment states that if the two statements are true:

1. If ##p##, then ##q##
2. ##p##

then we can conclude a third statement ====>##q##

Example:

1. If the whale is a mammal (##p##), then it has teats (##q##).
2. The whale is a mammal (##p##).

Conclusion: The whale has teats (##q##).

The Law of Syllogism states that if one thing implies the second, and the second implies the third, then we can conclude that the first implies the third.

1. If ##p##, then ##q##.
2. If ##q##, then ##r##

Conclusion: ##p##, therefore ##r##.

Example:

1. If Leah is intelligent (##p##), then she is an honor pupil (##q##).
2. If she is an honor pupil (##q##), then she is under a scholarship grant (##r##).

Conclusion:

Leah is intelligent (##p##), therefore she is under a scholarship grant (##r##).