# Symbolic Logic : First-Order Logic

## Example Questions

### Example Question #1 : First Order Logic

Identify the complex sentence of the following statement:

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

Explanation:

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

Recall the following logic symbols.

means "not"

means "implies"

means "or"

means "and"

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

Statement 2: Sally sells her basketball to her friend 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:

### Example Question #2 : First Order Logic

Identify the complex sentence of the following statement:

Sally has a cake 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.

means "not"

means "implies"

means "or"

means "and"

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

Statement 2: Sally sells her cake to her friend 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:

### Example Question #3 : First Order Logic

Identify the statement that corresponds to the following complex sentence:

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

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

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

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

Jane and Betty both have a bike.

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.

means "not"

means "implies"

means "or"

means "and"

means "equivalent"

For this particular problem the starting complex sentence is,

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

Statement 1:

"Jane no longer owns a bike"

Statement 2:

"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

in English terms becomes,

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