Some S are not M.

Some S are P.

Invalid; denying the antecedent

5) If something is a P, then it is not an M.

If something is an S, then it is an M.

If something is an S, then it is not a P.

Applying the law of contraposition on the first premise:

If something is an M, then it is not a P.

If something is an S, then it is not a P.

Valid; hypothetical syllogism

8) If something is a P, then it is an M.

Some S are not M.

Some S are P.

Invalid way of denying the consequent. What really follows is that some S are not P.

11) If something is a P, then it is not an M.

If something is an M, then it is an S.

If something is an S, then it is not a P.

Invalid form of hypothetical syllogism.

2) If office equipment is worth buying, it will make workers more productive.

Some computers will not make workers more productive.

Some computers are not worth buying.

Valid; denying the consequent

5) If a state ignores human rights, then it is a tyranny.

Some democracies ignore human rights.

Some democracies are tyrrannies.

Valid; affirming the antecedent.

8) If someone supported the voting rights bill, then they are opposed to racial discrimination.

If someone is a conservative, then they did not support the voting rights bill.

If someone is a conservative, then they do not oppose discrimination.

Invalid form of hypothetical syllogism

11) If a person overreacts to the charge that he is motivated by envy, then he is envious.

If a person has a strong sense of justice, then he is not envious.

If a person has a strong sense of justice, then he will not overreact to the charge of being envious.

Applying the law of contraposition to the first premise will give us:

If a person is not envious, then he will not overreact to the charge of being envious.

If a person has a strong sense of justice, the he is not envious.

If a person has a strong sense of justice, then he will not overreact to the charge of being envious.

Valid; hypothetical syllogism

2) If something is a material system, then it is governed by the laws of physics.

If something is a living system, then it is a material system.

If something is a living system then it is governed by the laws of physics.

Valid; hypothetical syllogism

5) If someone rejoices over victories, then they rejoice at the expense of others.

[If someone rejoices at the expense of others, then he cannot thrive in the world of men.]

If someone rejoices loudly over his victories, then he cannot thrive in the world of men.

Valid; hypothetical syllogism

8) He (Donald Newlove) fell asleep reading the "The Runaway Soul."

Some of the novels Newlove fell asleep reading are great.

"The Runaway Soul" is great.

Invalid; two particular premises. One might well think of this as a hasty generalization.