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# Using Logic to Determine Truth Value of Statements

1. p: Tanisha owns a convertible
q: Joan owns a Volvo

Translate each statement into symbols. Then construct a truth table for each and indicate under what conditions the compound statement is true.

Tanisha does not own a convertible but Joan owns a Volvo.

2. Determine whether the argument is valid or invalid. You may compare the argument to a standard form, given or use a truth table.

v &#8594;&#969;

&#969;/&#8756; &#8594; v

3. Write a negation of the statement.

She earns more than me.

4. Let p, q, and r be the following statements:

p: Jamie is on the train.
q: Sylvia is at the park.
r: Nigel is in the car.

Translate the following statement into English: (p V ~q)&#8594; ~r
1. p: Tanisha owns a convertible
q: Joan owns a Volvo

Translate each statement into symbols. Then construct a truth table for each and indicate under what conditions the compound statement is true.

Tanisha does not own a convertible but Joan owns a Volvo.

2. Determine whether the argument is valid or invalid. You may compare the argument to a standard form, given or use a truth table.

v &#8594;&#969;

&#969;/&#8756; &#8594; v

3. Write a negation of the statement.

She earns more than me.

4. Let p, q, and r be the following statements:

p: Jamie is on the train.
q: Sylvia is at the park.
r: Nigel is in the car.

Translate the following statement into English: (p V ~q)&#8594; ~r

#### Solution Preview

1. Tanisha does not own a convertible is the negation of p. Joan owns a Volvo is the statement q.

~p &#923; q

p q ~p ~p &#923; q
T T F F
T F F F
F T T T
F F T F

This compound statement is true ...

#### Solution Summary

Finding the truth value of statements using logic and truth tables.

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