Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument?

If it is July, then I am living at the lake.
I am not living at the lake.
Therefore, it is not July.

p: It is July.
q: I am living at the lake.

A) [(p → q) ∧ ~q]
∴ p

B)[(p → q) ∧ ~q]
∴ ~p

C)[(p → q) → q]
∴ p

D)[(p → q) ∧ q]
∴ p

Question

Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument?

  If it is July, then I am living at the lake.
  I am not living at the lake.
  Therefore, it is not July.

  p: It is July.
  q: I am living at the lake.

A)	[(p → q) ∧ ~q] 
∴ p

B)[(p → q) ∧ ~q] 
∴ ~p

C)[(p → q) → q] 
∴ p

D)[(p → q) ∧ q] 
∴ p

inkyvoyd · Answer

do you understand the notation here?

anonymous · Answer

no i do not.

inkyvoyd · Answer

∴ means therefore
~ means not.
^ means AND
→ means IMPLIES

inkyvoyd · Answer

so, what do you think the first statement "  If it is July, then I am living at the lake." would be translated as?

anonymous · Answer

well i think the answer would be D but im not to sure

inkyvoyd · Answer

What leads you to think the answer is D? I thought you said you didn't understand the notation

anonymous · Answer

after looking at the notation, im trying to figure out the answer

inkyvoyd · Answer

here, try to translate the statements one by one.
what do you think the first statement
 If it is July, then I am living at the lake.
can be translated as?

anonymous · Answer

wouldn't the first part just stay the same as [(p → q)

inkyvoyd · Answer

okay. What about the second part?
  I am not living at the lake.

anonymous · Answer

∧ ~q]

inkyvoyd · Answer

okay. so we have 
[(p → q) ∧ ~q]

inkyvoyd · Answer

"Therefore, it is not July." what would that be?

anonymous · Answer

[(p → q) ∧ ~q] 
∴ ~p

inkyvoyd · Answer

yeah

inkyvoyd · Answer

btw, that kind of argument is called modus tollens

inkyvoyd · Answer

http://en.wikipedia.org/wiki/Modus_tollens

anonymous · Answer

thank you so much :)!

inkyvoyd · Answer

no problem :)

anonymous · Answer

Which of the following truth tables shows the statement ~p → ~q ?
	
 p 	 q 	 ~p 	 ~q 	 ~p → ~q 
T	T	F	T	T
T	F	F	F	T
F	T	T	T	T
F	F	T	F	F
	
 p 	 q 	 ~p 	 ~q 	 ~p → ~q 
T	T	F	F	T
T	F	F	T	F
F	T	T	F	F
F	F	T	T	T
	
 p 	 q 	 ~p 	 ~q 	 ~p → ~q 
T	T	F	F	F
T	F	F	T	T
F	T	T	F	F
F	F	T	T	T
	
 p 	 q 	 ~p 	 ~q 	 ~p → ~q 
T	T	F	F	T
T	F	F	T	T
F	T	T	F	F
F	F	T	T	T

inkyvoyd · Answer

oh dear. post a new question for that one :)

anonymous · Answer

haha alright :D sounds good i ment too lol