# About Truth Tables

Using the Internet and other resources define and study Truth Tables. How are Truth Tables used in computer programming? Give a short example. Did you find other areas where Truth Tables are used? Explain.

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#### Solution Preview

Hi,

Truth tables are mathematical tables used in logic analysis. A truth table consists of logical representations of 1 or more inputs and the equivalent output from the combination of inputs. For example, there are 2 inputs, A and B. When both inputs are 1 (other meanings of 1 are HIGH, TRUE and ON), that is the only time the output F will have an output of 0 (other meanings of 0 are LOW, FALSE and OFF). When we write this in a table:

A | B | F |

0 0 1

0 1 1

1 0 1

1 1 0

From that table, we can formulate the process to produce output F from inputs A and B:

F = A' + B'

where the apostrophe symbol means the complement of the input (complement of 1 is 0 and vice-versa)

Logic mathematics are composed of logic gates, which represent a process in Boolean algebra. ...

#### Solution Summary

This posting contains answers to the given questions.

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.