# Math Test

1.  Write the negation of the statement – No sedans have three wheels.
2. 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°.

1. 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.

1. 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.

1. Determine whether the following statement is a tautology, self-contradiction or neither   —    pΛ (q ↔  ~q)
2. 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.

1. 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.

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

p → q,    ~q →  ~p

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

~ (p Λ q),   ~q ~p

1.    Determine which if any of the following statements are equivalent
1.   The pay is good and today is Monday
2.   If I take the job, then the pay is good or today is Monday
3.   The pay is good and Today is Monday, or I will take the job
4.    Determine whether the argument is valid or invalid.

r ↔ p

q ∨ r

p ∨ r

1.   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

1.    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

1.    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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