# 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.

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