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Disjunction Based Logic Tables

HSG-MG.A.3
Answer Keys Here

Aligned To Common Core Standard:

High School Geometry - HSG-MG.A.3

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.

Printable Worksheets And Lessons


  • 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.


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?