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Flashcards: First-Order Logic

Identify the complex sentence of the following statement:

Sally has a basketball and she sells it to her friend Bob.

$\text{Own(Sally, Basketball, Bob) }\Rightarrow \lnot\text{Sold(Sally, Basketball)}$

$\text{Sold(Sally, Basketball, Bob) }\Rightarrow \lnot\text{Owns(Sally, Basketball)}$

$\lnot\text{Sold(Sally, Basketball, Bob) }\Rightarrow \text{Owns(Sally, Basketball)}$

$\text{Own(Sally, Basketball, Bob) }\Rightarrow \text{Sold(Sally, Basketball)}$

$\text{Sold(Sally, Basketball, Bob) }\Rightarrow \text{Owns(Sally, Basketball)}$

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Flashcards: First-Order Logic

Sally has a basketball and she sells it to her friend Bob.

Your answer:

$\text{Own(Sally, Basketball, Bob) }\Rightarrow \lnot\text{Sold(Sally, Basketball)}$

Your answer:

$\lnot\text{Sold(Sally, Basketball, Bob) }\Rightarrow \text{Owns(Sally, Basketball)}$

Your answer:

$\text{Own(Sally, Basketball, Bob) }\Rightarrow \text{Sold(Sally, Basketball)}$

Your answer:

$\text{Sold(Sally, Basketball, Bob) }\Rightarrow \text{Owns(Sally, Basketball)}$

Correct answer:

$\text{Sold(Sally, Basketball, Bob) }\Rightarrow \lnot\text{Owns(Sally, Basketball)}$

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 basketball and she sells it to her friend Bob."

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 basketball

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

Statement 2: Sally sells her basketball to her friend Bob.

$\text{Sold(Sally, basketball, Bob)}$

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

$\text{Sold(Sally, Basketball, Bob) }\Rightarrow \lnot\text{Owns(Sally, Basketball)}$

Flashcards: First-Order Logic

Identify the complex sentence of the following statement:

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

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

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

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

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

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

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Flashcards: First-Order Logic

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

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: First-Order Logic

Flashcards: First-Order Logic

Flashcards: First-Order Logic

Flashcards: First-Order Logic

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HIGH SCHOOL

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All Symbolic Logic Resources

Flashcards: First-Order Logic

Flashcards: First-Order Logic

Flashcards: First-Order Logic

Flashcards: First-Order Logic

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

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