# Math

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Please I am having a hard time with these.

Let p be: it is wrong to smoke in public

Let q be: secondary cigarette smoke is a health threat

Let r be: the American Lung Association says that secondary cigarette smoke is a health threat

A. What would ~q be in words?
B. Change the first statement (It is wrong to smoke in public if secondary cigarette smoke is a health threat.) to symbols.
C. What is the symbolic representation of the second statement (If secondary cigarette smoke were not a health threat, the American lung Association would not say that it is)?
D. What is a simpler equivalent symbolic statement for the second statement?
E. What is the symbolic representation of the third statement (The American lung Association says that secondary cigarette smoke is a health threat)?
F. What is the symbolic representation of the conclusion(Therefore, it is wrong to smoke in public)?
G. Is this argument Valid or Invalid?

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