# Conditionals Using Logic Tables Worksheets

A conditional statement is a consequential declaration which means when certain terms are met it will result in one output or another. They are commonly referred to as (if-then) logic statements. These simple assertions form the foundation of computer science. A series of these statements can be used to evaluate an entire system. When analyzed by a computer, you can basically teach a computer what to do when certain situations arise. Artificial intelligence (AI) is based on this form of math with the use of very complex matrices. These worksheets and lesson will help students learn how to understand logic statements that are directed by conditions.

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

- Statement to Table Step-by-Step Lesson- We give you a basic statement and ask you to create an entire truth table from it.
- Guided Lesson - You have a whole bunch of truth tables to write with a baseball player watching.
- Guided Lesson Explanation - When you see the actual tables in front of you, this starts to make a lot of sense.
- Practice Worksheet - You are definitely going to need paper for this one. I was going to provide a blank template, but teachers told me that they wouldn't use it.
- Matching Worksheet - Find the truth table and statement that goes together.

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

### Homework Sheets

Help students identify the implications of each symbol used in the tables.

- Homework 1 - They are false only when the “if; statement is true and the “then” statement is false.
- Homework 2 - If the original is true, the ∼ statement is false, and if the original is false, the ∼ statement is true.
- Homework 3 - In a truth table the original statement of ∼A is true, then ∼A is false.

### Practice Worksheets

The next standard begins to making these into word problems.

- Practice 1 - Conditionals are usually shaped in the sentence form of if-then.
- Practice 2 - Make a truth table for the statements: G → (∼H)
- Practice 3 - The → symbol is used to symbolize a relationship called material implication; a compound statement formed with this connective is true unless the component on the left (the antecedent) is true and the component on the right (the consequent) is false.

### Math Skill Quizzes

Many students find the second quiz to be the most difficult. It wasn't intended that way.

- Quiz 1 - See how well you grasp what is being passed at you.
- Quiz 2 - Get the logic down to get this completely filled out.
- Quiz 3 - Why stress over these at all.

### What Are Conditionals in Logic Tables?

A conditional statement is an if-then statement. This means that the output is not predetermined and depends on the condition that is present. It is made up of two simple sentences. One is a hypothesis represented by p and the other is a conclusion represented by q. The truth tables use these statements in combination and layout all the possibilities in the truth table. The hypothesis and conclusions are used in combination with the truth table to figure out the overall truth of the conditional statement.

The connector used in Conditional statements is and arrow ->.

The statements are connected like; p -> q which reads if 'p' then 'q' or 'p implies q'.

We use logic tables to display all the possible inputs and the outputs that results. This allows us to get a quick summation of where everything that is going on with a conditional. These truth tables display four distinct possibilities that are based on the truth value of the combination of the hypothesis and the conclusion.

It is to note that p -> q is true in the following conditions; When both the hypothesis (p) and conclusion (q) are true. When hypothesis (p) is false, but the conclusion (q) is true. When both hypotheses (p) and conclusion (q) are false. And p -> q is only false when the conclusion (q) is false.