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Flashcards: Symbolic Logic

Identify the statement that corresponds to the following complex sentence:

$\text{Sold(Jane, Bike, Betty) }\Rightarrow \lnot\text{Owns(Jane, Bike)}$

Jane and Betty both have a bike.

Betty has a bike and she sells it to her friend Jane.

Jane has a bike and she does not sells it to her friend Betty.

Jane has a bike and she sells it to her friend Betty.

Jane has a bike that she bought from her friend Betty.

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Flashcards: Symbolic Logic

$\text{Sold(Jane, Bike, Betty) }\Rightarrow \lnot\text{Owns(Jane, Bike)}$

Your answer:

Jane and Betty both have a bike.

Your answer:

Betty has a bike and she sells it to her friend Jane.

Your answer:

Jane has a bike and she does not sells it to her friend Betty.

Your answer:

Jane has a bike that she bought from her friend Betty.

Correct answer:

Jane has a bike and she sells it to her friend Betty.

Explanation:

First-order logic statements can be described in complex sentences by using logic symbols.

Recall the following logic symbols.

$\lnot$ means "not"

$\Rightarrow$ means "implies"

$\vee$ means "or"

$\wedge$ means "and"

$\Leftrightarrow$ means "equivalent"

For this particular problem the starting complex sentence is,

$\text{Sold(Jane, Bike, Betty) }\Rightarrow \lnot\text{Owns(Jane, Bike)}$

First, identify the first-order statements and write them in English form. This particular sentence has two first-order statements.

Statement 1: $\lnot\text{Owns(Jane, Bike)}$

"Jane no longer owns a bike"

Statement 2: $\text{Sold(Jane, Bike, Betty)}$

"Jane sold her bike to Betty"

To combine these statements into one sentence, it needs to be understood that once sells her bike she no longer has it therefore, the statement

$\text{Sold(Jane, Bike, Betty) }\Rightarrow \lnot\text{Owns(Jane, Bike)}$

in English terms becomes,

"Jane has a bike and she sells it to her friend Betty."

Flashcards: Symbolic Logic

Identify the complex sentence of the following statement:

Sally has a cake and she sells it to her friend Betty.

$\lnot\text{Sold(Sally, Cake, Betty) }\Rightarrow \text{Owns(Sally, Cake)}$

$\text{Sold(Sally, Cake, Betty) }\Leftrightarrow \lnot\text{Owns(Sally, Cake)}$

$\text{Sold(Sally, Cake, Betty) }\Rightarrow \text{Owns(Sally, Cake)}$

$\lnot\text{Sold(Sally, Cake, Betty) }\Rightarrow \lnot\text{Owns(Sally, Cake)}$

$\text{Sold(Sally, Cake, Betty) }\Rightarrow \lnot\text{Owns(Sally, Cake)}$

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Flashcards: Symbolic Logic

Sally has a cake and she sells it to her friend Betty.

Your answer:

$\lnot\text{Sold(Sally, Cake, Betty) }\Rightarrow \text{Owns(Sally, Cake)}$

Your answer:

$\text{Sold(Sally, Cake, Betty) }\Leftrightarrow \lnot\text{Owns(Sally, Cake)}$

Your answer:

$\text{Sold(Sally, Cake, Betty) }\Rightarrow \text{Owns(Sally, Cake)}$

Your answer:

$\lnot\text{Sold(Sally, Cake, Betty) }\Rightarrow \lnot\text{Owns(Sally, Cake)}$

Correct answer:

$\text{Sold(Sally, Cake, Betty) }\Rightarrow \lnot\text{Owns(Sally, Cake)}$

Explanation:

First-order logic statements can be described in complex sentences by using logic symbols.

Recall the following logic symbols.

$\lnot$ means "not"

$\Rightarrow$ means "implies"

$\vee$ means "or"

$\wedge$ means "and"

$\Leftrightarrow$ means "equivalent"

For this particular problem the starting sentence is,

"Sally has a cake and she sells it to her friend Betty."

First, identify the first-order statements and write them in symbolic form. This particular sentence has two first-order statements.

Statement 1: Sally has a cake

$\text{Owns(Sally, Cake)}$

Statement 2: Sally sells her cake to her friend Betty.

$\text{Sold(Sally, cake, Betty)}$

To combine these statements into one complex sentence, it needs to be understood that once Sally sells her cake she no longer has it therefore, the statement becomes:

$\text{Sold(Sally, Cake, Betty) }\Rightarrow \lnot\text{Owns(Sally, Cake)}$

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Flashcards: Symbolic Logic

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Flashcards: Symbolic Logic

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Flashcards: Symbolic Logic

Flashcards: Symbolic Logic

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