# Symbolic Logic : Sentential Logic

## Example Questions

### Example Question #1 : Symbolic Logic

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

If  and  are formulas then  is a formula as well.

If  and  are formulas then  is a formula as well.

If  and  are formulas then  is a formula as well.

Only , and  are formulas.

If  is a formula then  is a formula as well.

Only , and  are formulas.

Explanation:

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### Example Question #2 : Symbolic Logic

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

Only , and  are formulas.

If  and  are formulas then  is a formula as well.

If  is a formula then  is a formula as well.

If  and  are formulas then  is a formula as well.

If  and  are formulas then  is a formula as well.

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  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.

### Example Question #3 : Symbolic Logic

Which of the following statements is part of the definition for sentential logic?

If  is a formula then so is .

Every lower case letter is a formula.

If  is a formula then so is .

If  and  are formulas then  is a formula as well.

Anything and everything can be considered a formula.

If  and  are formulas then  is a formula as well.

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  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.