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Basic Logic - Example Arguments

In the following propositions, most of the major premises are worded as conditional statements:
IF <antecedent condition> THEN <consequent result>

Which of the following arguments are Valid and which are Invalid?

(The last problem relates directly to testing!)


If I stand in the rain, then I’ll get wet.
I am standing in the rain.
Therefore, I am wet.

   


If I stand in the rain, then I’ll get wet.
I am wet.
Therefore I am standing in the rain.

   


If I stand in the rain, thenI’ll get wet.
I am standing in the rain.
Therefore I am not wet.

   


If I stand in the rain, thenI’ll get dry.
I am standing in the rain.
Therefore I will get dry.

   


Some humans have 2 eyes.
I am human.
Therefore I have 2 eyes.

   


All humans have 2 eyes.
I have 2 eyes.
Therefore I am human.

   


AND - the big one that relates to testing:

If the system works correctly, then I will get the expected results.
I got the expected results.
Therefore the system works correctly.

   


Remember: If there is NO case in which the premises can be true, then the argument is still valid! That is because for an argument to be invalid, the premises must be true but the conclusion false. Therefore, if the premises cannot be true, then there can never be an instance in which the premises are true and the conclusion is false; in other words, if the argument can never be invalid – then it has to be valid! This is also another way of saying Garbage In – Garbage out.