# Complete the Truth Table Worksheets

What Are Math Truth Tables? A mathematical truth table is a table based on the truth or false of a compound statement. In a mathematical truth table, we represent statements in the form of a letter or variable, like p, q, or r, and every statement has its own corresponding column. These columns in the truth table mention down all the possible truth values. In our daily life, we do not construct truth tables. However, we use logical reasoning and built truth tables to evaluate whether the statement falls in the truth column or false. Consider this example from our everyday life; 'If it is raining outside, then the football game is cancelled.' This statement will now be put in the truth table to check how true it is. This requires giving input to the statement. If it is raining outside = p, If it is not raining outside = not p. The truth table will be constructed as; if it rained outside, then not p is false, or if it didn't rain outside then not p is true. The truth tables also involve conjunction, disjunction, and implication statements. These worksheets and lessons help students learn to model all the possible outcomes of a situation mathematically.

### Aligned Standard: HSG-MG.A.3

- Conjugation Table Step-by-Step Lesson- We start you with table that examines conjugation and is missing some parts.
- Guided Lesson - This is a very slow progression for you into the concepts that are presented here.
- Guided Lesson Explanation - With all truth tables, I like to work an open logic table and then pick it apart.
- Practice Worksheet - After completing these problems should really understand the concepts well.
- Matching Worksheet - I intended this one to be a warm up for students or a quick review.
- Completing Truth Tables Five Pack of Worksheets - All you need to do is make each statement complete. Sounds easy enough.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

You should have your truth tables down solid after completing these.

- Homework 1 - Before completing the truth table first we have to look for some statements. The symbol ^ denotes that conjugation is taking place.
- Homework 2 - In order for a conjugation to be true both statements must be true, otherwise it is false. If we look at the table we just need to fill in the missing parts.
- Homework 3 - Take your time with these problems.

### Practice Worksheets

The practice sheets are bit more difficult as they are not directed.

- Practice 1 - If the original is true, the ∼ statement is false, and if the original is false, the ∼ statement is true.
- Practice 2 - "^" symbolizes logical conjunction; a compound statement formed with this connective is true only if both of the component statements between which it occurs are true.
- Practice 3 - In truth table the original component statements between which it occurs are true, than the statement is true.

### Math Skill Quizzes

We narrowed down the scope of the questions in the quizzes.

- Quiz 1 - Complete the truth table when you standard argument follows this lead: A^ ∼ B
- Quiz 2 - Make this one go the distance. This is a real mix of problems for you to work with.
- Quiz 3 - In truth table the original component statements between which it occurs are true, than the statement is true.

### Where is This Skill Used in The Real World?

It is ironic that many people do not see a great deal of logic in studying mathematics. It is difficult to see where you need to use this skill in your everyday life and outside of these exercises that teachers run you through repeatedly. The goal behind any series of truth tables is to analyze an argument or position that someone is asserting. This argument could be explaining an unidentified flying object (UFO) in the sky is or what happened in legal case. This form of reasoning is used to breakdown the thoughts behind creating new laws and interpreting legal contracts. It can also be used be electricians to manage the flow of electricity through a home or building. Plumbers do the same thing for the flow of water. When business analysts attempt to predict or forecast the future success of a company, they will often use this format of logic to make their assessment. Anytime you need to have a clear and objective look at an argument of some type, this is your go to math tool.

This form of logic and notation has huge applications in both and type of computer science, psychology, and philosophy. As humans race to digitize medicine and functions of it we see that the root of all computer programs that are based on this type of logic. You may have seen flowcharts that provide a visual form of diagnostics in the office of a physician. They all start out by asking where it hurts to identify an organ system to breakdown. Once that has been identified they attempt to understand the exact alignment based on a series of questions. This may seem very familiar to course of action that doctors take when you go for a visit. Yes, this form of math is attempting to reduce the number of physicians that will be needed in the future. We find this is a prevalent area of growth throughout the medical industry.