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Flashcards: Sentential Logic

Which of the following statements is NOT a definition of sentential logic?

If and are formulas then $A\vee B$ is a formula as well.

If and are formulas then $A\Leftrightarrow B$ is a formula as well.

If is a formula then $\sim A$ is a formula as well.

If and are formulas then $A\rightarrow B$ is a formula as well.

Only , , , and are formulas.

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Flashcards: Sentential Logic

Which of the following statements is NOT a definition of sentential logic?

Your answer:

If and are formulas then $A\vee B$ is a formula as well.

Your answer:

If and are formulas then $A\Leftrightarrow B$ is a formula as well.

Your answer:

If is a formula then $\sim A$ is a formula as well.

Your answer:

If and are formulas then $A\rightarrow B$ is a formula as well.

Correct answer:

Only , , , and are formulas.

Explanation:

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 $\sim A$ is a formula as well.

II. If and are formulas then $A\vee B$ is a formula as well.

III. If and are formulas then $A\rightarrow B$ is a formula as well.

IV. If and are formulas then $A\Leftrightarrow B$ is a formula as well.

V. If and are formulas then $A\wedge B$ 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.

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Flashcards: Sentential Logic

Flashcards: Sentential Logic

Flashcards: Sentential Logic

Flashcards: Sentential Logic

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Flashcards: Sentential Logic

Flashcards: Sentential Logic

Flashcards: Sentential Logic

Flashcards: Sentential Logic

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