Logic Propositions: Valid and Invalid Arguments

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The discussion focuses on solving logical propositions and determining the validity of arguments. For the first section, participants express propositions as equations or inequalities using Venn diagrams. The responses indicate that all merchants are speculators (MS=0 with a bar over S), some stockholders advising customers are not partners (SP=0 with a bar over P and a line through the equal sign), and no pipelines across foreign territories are safe investments (PS=0 with a bar over S). In the second section, the validity of two arguments is assessed. The first argument, stating that if it is raining, then the ground is wet, is deemed valid as it follows the modus ponens logical structure. The second argument, which claims that if the roads are not slippery, then it is not snowing, is labeled invalid because it does not adhere to the modus tollens logical form. The discussion emphasizes the importance of logical reasoning in evaluating propositions and arguments.
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Hello to all. Could anyone give me some insight on the following problems? I put my answers down, but not sure if they are correct. Thanks for any help you may provide.

A. Express each of the following propositions as equations or inequalities, representing each class by the first letter of the English term designating it, and symbolizing the proposition by means of a Venn diagram:

1. All merchants are speculators. Answer: MS=0 (with bar over the "S")
2. Some stockholders who advise their customers about making investments are not partners in companies whose securities they recommend. Answer: SP=0 (bar over "P" & line thru the equal sign)
3. No pipelines laid across foreign territories are safe investments. Answer: PS=0
 
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(bar over "S")

B. Determine whether the following arguments are valid or invalid:

1. If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.

This argument is valid. It follows the logical form of modus ponens, where the first statement (if it is raining, then the ground is wet) is the premise, the second statement (it is raining) is the premise, and the conclusion (the ground is wet) follows logically from the premises.

2. If it is snowing, then the roads are slippery. The roads are not slippery. Therefore, it is not snowing.

This argument is invalid. It does not follow the logical form of modus tollens, where the first statement (if it is snowing, then the roads are slippery) is the premise, the second statement (the roads are not slippery) is the premise, and the conclusion (it is not snowing) does not logically follow from the premises.
 

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