# Symbolic Logic: Modus Ponens and Modus Tollens

Symbolic Logic

PART 1

1. Write two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives. (If your computer does not have all the symbols needed, use some other symbol you do have access to and explain what its meaning is.)

2. What advantages does being able to symbolize our arguments provide?

3. Are there disadvantages to using this technique to make the structure of our arguments more explicit and clear?

PART 2

Imagine someone asks you what you have learned in your logic class and what you found to be the most useful information you learned there.

1. Is it important for people to study logic?

2. What kinds of mistakes might they make without having been exposed to a careful study of reasoning provided by logic?

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Predicate logic

PREDICATE LOGIC

Note: For your convenience the truth tables are included. You may not need to use all of the columns in the skeleton tables.

1. Use modus ponens or modus tollens to fill in the blanks in the arguments so as to produce a valid inference.

If this polygon is a triangle, then the sum of its interior angles is 180.

The sum of the interior angles of this polygon is not 180.

______________________________________

Form: modus__________

Use truth table to determine whether the argument forms in 2 and 3 are valid.

2. p q

p r

p q r

p Q r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Final answer and explanation: _________________________

3. p ~q r

p q

q p

r

p Q R

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Final answer and explanation: _________________________

4. Use symbols to write the logical form for the following exercise, and then use the truth table to test the argument for validity.

Oleg is a math major or Oleg is an economics major.

If Oleg is a math major, then Oleg is required to take a Math 362.

Oleg is an economics major or Oleg is not required to take a Math 362.

p: _________________________

q: _________________________

r: _________________________

Argument in symbolic form:

_________________________

_________________________

_________________________

p q r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Final answer and explanation: _________________________

5. Use symbols to write the logical form of the following argument. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise state whether the converse or inverse error is made.

If this computer program is correct, then it produces the correct output when run with the test data my teacher gave me.

This computer program produces the correct output when run with the test data my teacher gave me.

This computer program is correct.

p: _________________________________________________

q: _________________________________________________

Possible argument forms are (choose the appropriate one):

p q

p

q

p q

~q

~p

p q

q

p

p q

~p

~q

Argument form: (copy and paste the appropriate form listed above)

Valid or invalid? _____________________________________________

Argument type? ______________________________________________

(choose modus ponens, modus tollens, inverse error, or converse error)