Compound Statements Worksheets
When two simple statement components are connected in some way or other, we refer to them as compound statements or propositions. To determine if the overall proposition is true or false, you need to contemplate a great deal. We call this state of being overall true or false the truth value. To ascertain this, it all begins with evaluating each of the simple statements or propositions. You determine the truth value of each of those first then you move on to evaluate the relationship that exists between those propositions. So, as you see, this is a three-step process. These worksheets help students understate the truth value of various compound statements. We will also examine how to chart these truth values and how to interpret premade charts that display this.
Aligned Standard: HSG-MG.A.3
- Number Sentences Step-by-Step Lesson- Compound sentences do make it a bit more tricky to understand.
- Guided Lesson - Did you know that tigers can fly in logic? No they can't!
- Guided Lesson Explanation - The basic strategy is to identify the truth value of each part of the sentence and then apply it to all.
- Practice Worksheet - I have no idea why I so obsessed with prime numbers, but I am.
- Matching Worksheet - See what the kids think about the way these are answered. Remind students that they learned the word "cardinal" in second grade.
- Truth Values of Compound Sentences Five Pack of Worksheets - Make sure not to get thrown by the use of angle dimensions; at times.
- Answer Keys - These are for all the unlocked materials above.
All of the sentence are mathematical based sentences.
- Homework 1 - We have a compound sentence here. That means that it has two or more parts that must both be true in order for the statement to be deemed true.
- Homework 2 - Since both facts are true, the entire sentence is true.
- Homework 3 - If 6 and 8 are even, then tigers swim.
Tigers fly? That's what students told me the second I handed them these!
- Practice 1 - Now let's look at both statements and determine their individual truth value.
- Practice 2 - Since a portion of the compound sentence is false, the entire sentence is false.
- Practice 3 - If 5 and 7 are odd, then shoes run.
Math Skill Quizzes
I used short sentences here to make sure the wording didn't get in the way.
- Quiz 1 - 5 + 3 = 8 and 6 is a prime number.
- Quiz 2 - Determine the truth value of the statement: 7 - 3 = 4 and 2 is an even number.
- Quiz 3 - Since both facts are true, the entire sentence is true.
How to Judge the Truth Values of Compound Statements?
Compound statements, as the phrase, suggests deals with two or more sentences combined together by the use of an operator. Since there are two, often separate, thoughts that contribute to the overall system of these propositions there is a three-step process in order to evaluate the truth value of compound statements. The first two steps require you to determine the truth value of each simple sentence. Once you have those values you then evaluate the relationship between those two propositions. There are five common relationships that you will find in logic:
Conjunction - When two simple sentences, we will call them p and q, are joined in a conjunction statement, both sentences should be satisfied in order for the overall statement to be true. These thoughts are joined by the use of the word (and). For example, Joe eats fries, and Maria drinks soda. Here, both sentences work collaboratively with each other. Now, both of these statements need to be true, and if they aren’t, then the compound statements will not become true.
Disjunction - In this relationship the components are joined by the term (or). In order for the overall proposition to be true, when the terms are joined by (or), just requires that one of the components be true. An example would be, "The sky is purple or blue!"
Conditional - This is a cool one, because they are always true except in one scenario. If the antecedent is true and the consequent, the overall proposition is false. These are presented a (if-then) propositions. In shorthand they are presented using an arrow (→).
Biconditional - This is an easy one to remember because in order to be true both components must be the same. This means that they either must both be true or both be false in order for the overall proposition to be true. They present with the (if and only if). You will see them displayed with the use of what is called a double arrow (↔). It looks more like an abbreviated line to me.
Negation - This is the logical polar opposite value of the statement or proposition.
You will also see come across instances where truth values are presented in binary code. This makes a nice transition to logic that you will use in computer science courses. The standard is to use (1) to indicate a value that is true and a (0) to indicate a false proposition.