3. Are all valid arguments sound? Why or why not? Give an example if necessary.
All sound arguments are valid arguments. But all valid arguments are not sound. An argument is said to be valid if all the premises are true then there is no way in which the conclusion can be false. However, an argument is sound, if the argument is valid and the premises are actually true.
Example where we have a valid argument that is not sound,
All pencils are made of
silver.
All silver things sparkle,
Therefore, all pencils sparkle.
In this, the premise cannot ever actually be true. But this argument stands valid.
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3. Are all valid arguments sound? Why or why not? Give an example if necessary.
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Discrete Mathematics 12. Consider the universe of all arguments. Let S(a): "a is sound." Let V(a): "a is valid." Let P(a): "the premise of a it true." Consider the sentence: Va(S(a)-V(a) AP(a)) (a) Interpret the symbolic sentence into a an English sentence. (b) Negate the symbolic sentence and simplify as much as possible. Your answer should be a symbolic sentence. (c) Write an English sentence for the symbolic sentence in part b. 12. Consider the universe of all arguments. Let...
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