# Determining whether logic statements are true or false.

Explain whether the following is true or false.

A. All reasonable arguments are true.

B. The claim "If it is raining, the exposed surfaces will be wet" is an argument composed of simple statements.

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These are tricky questions. You must think them through carefully.

A. All reasonable arguments are true. I think this statement is most likely. But it depends on what type of argument you are making. An empirical claim (one observed by facts) can be reasonable and false. But a reasonable analytical claim is always true. For example, an analytical claim is: all bachelors are unmarried men, Ben is not married, therefore Ben is a bachelor. If A and B are correct then the conclusion must be true. But empirical ...

#### Solution Summary

This job determines whether logic statements are true or false.

Constructing truth tables and interpreting logic statements.

I am asked to help set up a study group using sample study questions that gives some of us in the group the most trouble and I need help formulating these types of equations.

1. Determine the truth value of the following statement:

The Leaning Tower of Pisa is located in England and all prime numbers divisible by 1.

True or False

2. Construct a truth table for (p V q) → ~p

3. Fill in the heading of the following truth table using any of p, q, ~, →, ↔, V, and Λ.

P Q XXXXXXXX

T T F

T F T

F T F

F F F

4. Construct a truth table for ~p → (~p V q)

5. Given p is true, q is true, and r is false, find the truth value of the statement ~q → (~p Λ r). Show step by step work.

6. Determine which, if any, of the three statements are equivalent.

I) If the pipe is leaking, then I will not call the roofer.

II) Either the pipe is leaking or I will call the roofer.

III) If the pipe is not leaking, then I will call the roofer.

I and II are equivalent

II and III are equivalent

I and III are equivalent

I, II, and III are equivalent

None are equivalent

7. Write the argument below in symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used.

Either the gazebo is made of wood or the vine is growing on the gazebo.

The gazebo is not made of wood.

∴ The vine is growing on the gazebo.

P: The gazebo is made of wood.

Q: The vine is growing on the gazebo.