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It is important to recall that sentential logic has a very specific definition that outlines and describes different formulas.

There are seven different statement criteria when discussing sentential logic and they are as follows.

I. If  is a formula then  is a formula as well.

II. If  and  are formulas then  is a formula as well.

III. If  and  are formulas then  is a formula as well.

IV. If  and  are formulas then  is a formula as well.

V.  If  and  are formulas then  is a formula as well.

VI. All upper case letters are formulas

VII. Nothing else is a formula.

Looking at the possible answer selections, I, II, III, and IV are part of the sentential logic definition thus, "Only , , , and  are formulas." is NOT in the definition. This can be verified by part VI in the definition which states that all upper case letters are formulas.

It is important to recall that sentential logic has a very specific definition that outlines and describes different formulas.

There are seven different statement criteria when discussing sentential logic and they are as follows.

I. If  is a formula then  is a formula as well.

II. If  and  are formulas then  is a formula as well.

III. If  and  are formulas then  is a formula as well.

IV. If  and  are formulas then  is a formula as well.

V.  If  and  are formulas then  is a formula as well.

VI. All upper case letters are formulas

VII. Nothing else is a formula.

Looking at the possible answer selections only IV is part of the sentential logic definition thus, "If  and  are formulas then  is a formula as well." is in the definition.

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

 and  result in a true statement whenever the first constant is the same as the second constant. Therefore, the missing operator is "implies".

In mathematical terms the missing operator is .

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

 and  result in a true statement whenever one of the constants is true. Therefore, the missing operator is "or".

In mathematical terms the missing operator is .

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

The result is always opposite of the value of . Therefore, the missing operator is "not".

In mathematical terms the missing operator is .

Symbolic logic describes English statements using mathematical symbols. These mathematical symbols can be categorized into five areas.

I. Predicates: , 

II. Terms: Terms are the variables that represents the objects and constants of a statement.

III. Quantifiers: , 

IV. Punctuation: (,)

V. Connectives : , , , , , , 

This particular question asks to identify the "quantifier".

Since there are only two symbols that are categorized as "quantifiers",  and  ,and the "for all" symbol   is the only one present in the answer choices, that is the correct answer. 

Symbolic logic describes English statements using mathematical symbols. These mathematical symbols can be categorized into five areas.

I. Predicates: , 

II. Terms: Terms are the variables that represents the objects and constants of a statement.

III. Quantifiers: , 

IV. Punctuation: (,)

V. Connectives : , , , , , , 

This particular question asks to identify the "quantifier".

Since there are only two symbols that are categorized as "quantifiers",  and  ,and the "exists" symbol   is the only one present in the answer choices, that is the correct answer. 

Symbolic logic describes English statements using mathematical symbols. These mathematical symbols can be categorized into five areas.

I. Predicates: , 

II. Terms: Terms are the variables that represents the objects and constants of a statement.

III. Quantifiers: , 

IV. Punctuation: (,)

V. Connectives : , , , , , , 

This particular question asks to identify the "quantifier".

Since there are only two symbols that are categorized as "predicates",  and  ,and the "equal" symbol   is the only one present in the answer choices, that is the correct answer. 

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: