# Math Test

- Write the negation of the statement –
*No sedans have three wheels.* - Let p = The temperature ≥ 90°.

q = The air conditioner is working.

r = The apartment is not hot.

Write the following statement in symbolic form

If the apartment is hot and the air conditioner is working, then the

temperature ≥ 90°.

- Write the following statement in symbolic form and construct a truth table.

*It is false that Mr. Chen is the president or that Ms. Chow is not the *

* treasurer.*

- Let p = Sam owns a sedan.

q = Joan owns an SUV.

Translate the following statement into symbols. Then determine under what conditions the compound statement is true. Note: A truth table may be needed.

*Sam does not own a sedan, but Joan does not own a SUV.*

- Determine whether the following statement is a tautology, self-contradiction or neither — pΛ (q ↔ ~q)
- Refer to Figure T2-6 on the “Test No 2 Information and Fact-Concept Sheet”.

Determine the truth value of the simple statements then determine the truth value of the compound statement.

* Io has a diameter of 1000-3161 miles or Thebe may not have water, and Io*

* may have atmosphere.*

- Let p = False – Mike spoke at the engineer’s conference

q = True – Mike received the outstanding engineer’s award

Find the truth value of the compound statement –

*If Mike did not receive the outstanding engineers award, then Mike did not speak at the engineer’s conference.*

- Use a truth table to determine whether the two statements are equivalent.

p → q, ~q → ~p

- Use De Morgan’s Laws to determine whether the two statements are equivalent

~ (p Λ q), ~q**∨** ~p

- Determine which if any of the following statements are equivalent

- The pay is good and today is Monday
- If I take the job, then the pay is good or today is Monday
- The pay is good and Today is Monday, or I will take the job
- Determine whether the argument is valid or invalid.

r ↔ p

q ∨ r

**∴** p ∨ r

- Translate the argument into symbolic and then determine whether the argument

is valid or invalid.

If you pass general chemistry then you can take organic chemistry.

You pass general chemistry.

**∴** You can not take organic chemistry

- Use an Euler Diagram to determine whether the syllogism is valid or invalid.

Some skunks are not tame

Stinky is a skunk

**∴** Stinky is not tame

- Use an Euler Diagram to determine whether the syllogism is valid or invalid.

Some dogs wear glasses

Fido does not wear glasses

**∴** Fido is a dog

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