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
Can you answer these questions?
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?
Sure, I can help you with these questions.
A. "~q" in words would be "It is not the case that secondary cigarette smoke is a health threat."
B. The first statement "It is wrong to smoke in public if secondary cigarette smoke is a health threat" can be represented using symbols as "p → q". Here, "p" represents "It is wrong to smoke in public" and "q" represents "Secondary cigarette smoke is a health threat".
C. 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" can be written as "¬q → ¬r". Here, "q" represents "Secondary cigarette smoke is a health threat" and "r" represents "The American Lung Association says that secondary cigarette smoke is a health threat."
D. A simpler equivalent symbolic statement for the second statement would be "r → q". This statement is equivalent because it states that if the American Lung Association says that secondary cigarette smoke is a health threat ("r"), then secondary cigarette smoke is indeed a health threat ("q").
E. The symbolic representation of the third statement "The American Lung Association says that secondary cigarette smoke is a health threat" is simply "r". Here, "r" represents "The American Lung Association says that secondary cigarette smoke is a health threat."
F. The symbolic representation of the conclusion "Therefore, it is wrong to smoke in public" is "p".
G. To determine if the argument is valid or invalid, we need to analyze the logical relationship between the premises and the conclusion. Since the premises are in the form of conditional statements (if-then), the argument can be valid if the conclusion follows logically from the premises. Without additional information or given premises, it is not possible to determine if the argument is valid or invalid.