Question

Translate the following statements into propositional logic. In each case, I've provided a key for the simple/atomic statements. Use that key to identify the proper translation into the language of propositional logic. The notion for the logical connectives that I'm using is this: \~ (negation), & (conjunction), \(disjunction), \rightarrow (material conditional), and \leftrightarrow (material equivalence or biconditional). Your ice is not cold. (I) -If my stock portfolio is weak, then I am losing money. (S, L) My car does not look great, but it gets great gas mileage. (L, G) If you feel great, then you look great. (F, L) + My test score was high or I am mistaken. (H, M) You passed the exam only if you got at least a C. (P, C) Either candy or tobacco is bad for your teeth. (C, T) Bill is cold and Mary is late. (B, M) Today is Monday or today is Tuesday. (M, T) He is not a U.S. senator. (S) Toothpaste is good for your teeth, but tobacco is not. (P, T) Driving too fast is hazardous to your health; and so is driving without buckling up. (F, B) Pizza contains all the basic food groups if, and only if, you get it with anchovies. (P, A) Lava lamps are distracting, while music in the background is soothing. My room could use a good cleaning, but I am too lazy to do anything about it. (D, S, C, L)

          Translate the following statements into propositional logic. In each case, I've provided a key for the simple/atomic statements. Use that key to
identify the proper translation into the language of propositional logic. The notion for the logical connectives that I'm using is this: \~ (negation), &
(conjunction), \(disjunction), \rightarrow (material conditional), and \leftrightarrow (material equivalence or biconditional).
Your ice is not cold. (I)
-If my stock portfolio is weak, then I am losing money. (S, L)
My car does not look great, but it gets great gas mileage. (L,
G)
If you feel great, then you look great. (F, L)
+ My test score was high or I am mistaken. (H, M)
You passed the exam only if you got at least a C. (P, C)
Either candy or tobacco is bad for your teeth. (C, T)
Bill is cold and Mary is late. (B, M)
Today is Monday or today is Tuesday. (M, T)
He is not a U.S. senator. (S)
Toothpaste is good for your teeth, but tobacco is not. (P, T)
Driving too fast is hazardous to your health; and so is driving
without buckling up. (F, B)
Pizza contains all the basic food groups if, and only if, you get
it with anchovies. (P, A)
Lava lamps are distracting, while music in the background is
soothing. My room could use a good cleaning, but I am too
lazy to do anything about it. (D, S, C, L)

Translate the following statements into propositional logic. In each case, I've provided a key for the simple/atomic statements. Use that key to
identify the proper translation into the language of propositional logic. The notion for the logical connectives that I'm using is this: (̃negation),
(conjunction), disjunction), → (material conditional), and ↔ (material equivalence or biconditional).
Your ice is not cold. (I)
-If my stock portfolio is weak, then I am losing money. (S, L)
My car does not look great, but it gets great gas mileage. (L,
G)
If you feel great, then you look great. (F, L)
+ My test score was high or I am mistaken. (H, M)
You passed the exam only if you got at least a C. (P, C)
Either candy or tobacco is bad for your teeth. (C, T)
Bill is cold and Mary is late. (B, M)
Today is Monday or today is Tuesday. (M, T)
He is not a U.S. senator. (S)
Toothpaste is good for your teeth, but tobacco is not. (P, T)
Driving too fast is hazardous to your health; and so is driving
without buckling up. (F, B)
Pizza contains all the basic food groups if, and only if, you get
it with anchovies. (P, A)
Lava lamps are distracting, while music in the background is
soothing. My room could use a good cleaning, but I am too
lazy to do anything about it. (D, S, C, L)

Added by Asunci-N D.

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