# 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)

https://brainmass.com/math/recurrence-relation/predicate-logic-622717

## SOLUTION This solution is **FREE** courtesy of BrainMass!

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.

_This polygon is not a triangle______

Form: modus__tollens____

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 q r p q p r p q r

T T T T T T T

T T F F T F F

T F T F F T F

T F F F F F F

F T T T T T T

F T F F T T T

F F T F T T T

F F F F T T T

Final answer and explanation: The rows in which both the premises are true, and the conclusion in that row is also true. Hence the argument form is valid.

3. p ~q r

p q

q p

r

p Q R ~q p ~q p ~q r p q q p r

T T T F F T T T T

T T F F F T T T F

T F T T T T T T T

T F F T T F T T F

F T T F F T T F T

F T F F F T T F F

F F T T F T F T T

F F F T F T F T F

Final answer and explanation: One highlighted row shows that an argument of this form can have true premises and a false conclusion. Hence this form of argument is invalid.

Answer: Invalid

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: ___ Oleg is a math major ______________________

q: ___ Oleg is a economics major ______________________

r: ___ Oleg is required to take a Math 362__________

Argument in symbolic form:

p q

p r

q ~r

p q r ~r p q p r q ~r

T T T F T T T

T T F T T F T

T F T F T T F

T F F T T F T

F T T F T T T

F T F T T T T

F F T F F T F

F F F T F T T

Final answer and explanation: One highlighted row shows that an argument of this form can have true premises and a false conclusion. Hence this form of argument is invalid.

Answer: Invalid

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: computer program is correct

q: It produces the correct output when run with the test data my teacher gave me.

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)

p q

q

p

Valid or invalid? Invalid

Argument type? Converse error

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

https://brainmass.com/math/recurrence-relation/predicate-logic-622717