# Logic : Conjunctions, Disjunctions, and Biconditionals Worksheets

You will often be asked to assess the conditions of various thoughts, statements, or propositions that cross your desk as an adult. Up to this point in school you have been looking at simple sentences and are have been responsible for determining if something was true or false. There are instances where these statements will have several components and those components can form many different types of connections together. This create a situation where it is much more difficult to determine the truth value of a proposition. In this section we will look at three different types of connections between these simple statements. These worksheets and lessons help students learn how to interpret logic statements that include a form of conjunction, disjunction, or biconditional.

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

- Disjunction Step-by-Step Lesson- We kick it off with an or statement. Some kids get lost in the wording of this.
- Guided Lesson - These questions really run the gamut of what can be asked at this level.
- Guided Lesson Explanation - Help students first identify the purpose of the question, this really makes them grasp the skill faster.
- Practice Worksheet - I did not get bored at the end of this worksheet, I just wanted to include some number classification.
- Matching Worksheet - The answer key adjusts for mixed answers, I just wanted to remind them to read all the choices.

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

### Homework Sheets

You'll find a hw sheet for each skill here to allow you to focus on skills.

- Homework 1 - Disjunctions are true when just one or both of the sentences are true.
- Homework 2 - 9 is an even number if and only if two angles in an isosceles triangle are equal.
- Homework 3 - In logic, a conjunction is a compound sentence formed by combining two sentences (or fact 0 using the word "and.". A conjunction is true only when both sentences are true.

### Practice Worksheets

Again, a practice sheet for each individual skill.

- Practice 1 - If first fact is false or second fact is true, the entire sentence is true.
- Practice 2 - The overall truth is only true if both statements have the same truth value; otherwise the statement is false.
- Practice 3 - Since both sentence is true, the entire sentence is true.

### Math Skill Quizzes

Read them carefully because you can quickly get confused. I always tell students to read them twice, then proceed.

- Quiz 1 - What is the truth value of the statement? Orange is a color or 4 is even.
- Quiz 2 - 10 is an even number if and only if two angles in an equilateral triangle are equal.
- Quiz 3 - What is the truth value of the statement? 6 + 5 = 11 and cats can fly.

### In Logic What Are Conjunctions, Disjunctions, and Biconditionals?

There are many times in logic when we need to determine whether a statement or proposition is true or false. This is usually a very straight forward process, but when two simple statements form a relationship through some form of union between them, this can be a bit more complex. There are a number of different ways (most commonly five are explored) in which this union can be formed. We will examine the three most common forms of these relationships.

Conjunctions are statements that are commonly combined with the use of the word “and” which are used in logic or truth tables. They are compound statements and are represented using the word 'and' in between two simple sentences. For example, conjunction for two statements will be 'It is windy outside, and the plan is canceled.' Other words (also, although, but, yet) can be used to create the same connection but are used less often in both language and math. It is to note that this statement will only be false when both the statements are false. If either of the statement is true, the conjunction will be true.

Disjunctions, like conjunctions, are also compound statements used with a connector word 'or.' A disjunction statement is true when both or one of the disjunction statements are true. In this example, the disjunction will be; It is windy outside, or the plan is cancelled.

Biconditionals are statements that contain the phrase “if and only if”. These are very powerful statements saying explicitly that both the statements are interchangeable. If one is true, the other one automatically becomes true and if one is false, the other one becomes false too. This is reflected in the truth table, and when both the statements have the same truth values, the biconditional stands true.