# Disjunction Based Logic Tables

What Is Disjunction in Logic Tables? Disjunctions are used in truth tables as a compound statement represented with the word 'or.' A disjunction can only be true when one or both of the original statements given as disjunctions are true. In a disjunction statement, there is no if like we have in truth tables. In this example, the disjunction will be; It is raining outside, or the football game is cancelled. The above statement will only be true when p or q or both p and q will be true. Unlike conjunction, with a disjunction, to have it as false, both the statements have to be false else it will true in any case. Since disjunction are two statements that can be connected with a connector 'or' one way to remember this when or when not a disjunction will be true is to follow this mnemonic. If you find an 'And,' it points up, while 'or' points down. To understand it better, look at this example: P= 14 is prime, Q= 17 is prime, R= 18 is composite. Disjunction statements for each of these statements are: 14 is prime, or 17 is prime --> True. 14 is prime, or 18 is composite --> False. 17 is prime, or 18 is composite --> True. These worksheets will help students learn how to understand the truth values of disjunction based statements within a logic table.

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

- Disjunction Table Step-by-Step Lesson- Yeah, I'm at a loss as to why I threw a witch in there too! I think is was this past Halloween that inspired that one.
- Guided Lesson - The picture kind of signifies what I see in students faces when they are working on these types of problems.
- Guided Lesson Explanation - The upside down carrot always is quick to understand because truth is only valid when there are no lies at all.
- Practice Worksheet - I forget to throw any clip art in this one, not really! Two teachers asked me to remove them to offer up more space.
- Matching Worksheet - Pay attention to the table for number three. There is a debate raging between teachers as to whether my answer is correct.

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

### Homework Sheets

Make a series of truth tables based on the statements.

- Homework 1 - The symbol " V " signifies inclusive disjunction a V statement is true whenever either (or both) of its component statements is true; it is false only when both of them are false.
- Homework 2 - Disjunctions are true when just one of the other statements are true.
- Homework 3 - Disjunctions are only false when both statements are false.

### Practice Worksheets

We follow a similar pattern to what you have seen in the previous tables.

- Practice 1 - If the original is true, the ∼ statement is false, and if the original is false, the ∼ statement is true.
- Practice 2 - Make a truth table for the statements: ∼H V ∼M
- Practice 3 - If the original is true, the ∼ statement is false, and if the original is false, the ∼ statement is true.

### Math Skill Quizzes

The quizzes can take students long periods of time.

- Quiz 1 - In truth table original of ∼M is true, than ∼M is false.
- Quiz 2 - If the original is true, the ∼ statement is false, and if the original is false, the ∼ statement is true.
- Quiz 3 - Where did this table come from?