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If-then statement
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When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events. If we instead use facts, rules and definitions then it's called deductive reasoning.
We will explain this by using an example.
If you get good grades then you will get into a good college.
The part after the "if": you get good grades - is called a hypotheses and the part after the "then" - you will get into a good college - is called a conclusion.
Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.
This is noted as
$$p \to q$$
This is read - if p then q.
A conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said "if you get good grades then you will not get into a good college".
If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional.
Our conditional statement is: if a population consists of 50% men then 50% of the population must be women.
If we exchange the position of the hypothesis and the conclusion we get a converse statemen t: if a population consists of 50% women then 50% of the population must be men.
$$q\rightarrow p$$
If both statements are true or if both statements are false then the converse is true. A conditional and its converse do not mean the same thing
If we negate both the hypothesis and the conclusion we get a inverse statemen t: if a population do not consist of 50% men then the population do not consist of 50% women.
$$\sim p\rightarrow \: \sim q$$
The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse.
We could also negate a converse statement, this is called a contrapositive statemen t: if a population do not consist of 50% women then the population do not consist of 50% men.
$$\sim q\rightarrow \: \sim p$$
The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.
A pattern of reaoning is a true assumption if it always lead to a true conclusion. The most common patterns of reasoning are detachment and syllogism.
If we turn of the water in the shower, then the water will stop pouring.
If we call the first part p and the second part q then we know that p results in q. This means that if p is true then q will also be true. This is called the law of detachment and is noted:
$$\left [ (p \to q)\wedge p \right ] \to q$$
The law of syllogism tells us that if p → q and q → r then p → r is also true.
This is noted:
$$\left [ (p \to q)\wedge (q \to r ) \right ] \to (p \to r)$$
If the following statements are true:
If we turn of the water (p), then the water will stop pouring (q). If the water stops pouring (q) then we don't get wet any more (r).
Then the law of syllogism tells us that if we turn of the water (p) then we don't get wet (r) must be true.
Video lesson
Write a converse, inverse and contrapositive to the conditional
"If you eat a whole pint of ice cream, then you won't be hungry"
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Calcworkshop
Conditional Statement If Then's Defined in Geometry - 15+ Examples!
// Last Updated: January 21, 2020 - Watch Video //
In today’s geometry lesson , you’re going to learn all about conditional statements!
Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)
We’re going to walk through several examples to ensure you know what you’re doing.
In addition, this lesson will prepare you for deductive reasoning and two column proofs later on.
Here we go!
What are Conditional Statements?
To better understand deductive reasoning, we must first learn about conditional statements.
A conditional statement has two parts: hypothesis ( if ) and conclusion ( then ).
In fact, conditional statements are nothing more than “If-Then” statements!
Sometimes a picture helps form our hypothesis or conclusion. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.
But to verify statements are correct, we take a deeper look at our if-then statements. This is why we form the converse , inverse , and contrapositive of our conditional statements.
What is the Converse of a Statement?
Well, the converse is when we switch or interchange our hypothesis and conclusion.
Conditional Statement : “If today is Wednesday, then yesterday was Tuesday.”
Hypothesis : “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.”
So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.
Converse : “If yesterday was Tuesday, then today is Wednesday.”
What is the Inverse of a Statement?
Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement.
So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”.
Inverse : “If today is not Wednesday, then yesterday was not Tuesday.”
What is a Contrapositive?
And the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both.
Contrapositive : “If yesterday was not Tuesday, then today is not Wednesday”
What is a Biconditional Statement?
A statement written in “if and only if” form combines a reversible statement and its true converse. In other words the conditional statement and converse are both true.
Continuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”
Biconditional : “Today is Wednesday if and only if yesterday was Tuesday.”
Examples of Conditional Statements
In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. And here’s a big hint…
Whenever you see “con” that means you switch! It’s like being a con-artist!
Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.
After this lesson, we will be ready to tackle deductive reasoning head-on, and feel confident as we march onward toward learning two-column proofs!
Conditional Statements – Lesson & Examples (Video)
- Introduction to conditional statements
- 00:00:25 – What are conditional statements, converses, and biconditional statements? (Examples #1-2)
- 00:05:21 – Understanding venn diagrams (Examples #3-4)
- 00:11:07 – Supply the missing venn diagram and conditional statement for each question (Examples #5-8)
- Exclusive Content for Member’s Only
- 00:17:48 – Write the statement and converse then determine if they are reversible (Examples #9-12)
- 00:29:17 – Understanding the inverse, contrapositive, and symbol notation
- 00:35:33 – Write the statement, converse, inverse, contrapositive, and biconditional statements for each question (Examples #13-14)
- 00:45:40 – Using geometry postulates to verify statements (Example #15)
- 00:53:23 – What are perpendicular lines, perpendicular planes and the perpendicular bisector?
- 00:56:26 – Using the figure, determine if the statement is true or false (Example #16)
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions
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Geometry: Conditionals, Converses, and Biconditionals Practice Test2.2.1: I can identify. he part. ____ 1. point) h one line and circle the conclusion of this conditional statement:If two li. es intersect at right angles, then the two l. s are perpendicular.Hypothesis: The two lines a. e perpendicular. Conclusion: Two lines interse.
Follow us. Improve your math knowledge with free questions in "Identify hypotheses and conclusions" and thousands of other math skills.
The conclusion is the result of a hypothesis. Figure 2.11.1 2.11. 1. If-then statements might not always be written in the "if-then" form. Here are some examples of conditional statements: Statement 1: If you work overtime, then you'll be paid time-and-a-half. Statement 2: I'll wash the car if the weather is nice.
Conditional Statements and Converses. Conditional statements are routinely referred to as "if-then" statements. They are composed of two main parts the hypothesis (if) and the conclusion (then). Conditional statements are true unless they lead us to a false conclusion. We can form a converse statement by rearranging the hypothesis and the ...
Name_____ Geometry HW: 2.2 Worksheet Identify the hypothesis and conclusion of each conditional. 1. If you are an American citizen, then you have the right to vote. 2. If a figure is a rectangle, then it has four sides. 3. If you want to be healthy, then you should eat vegetables.
Geometry: 2.1-2.3 NotesGeometry: 2.1-2.3 Notes NAM. Conditional StatementA conditional statement is a logical statement that has two parts, a hypothes. s p and a conclusion q. When a conditional statement is written in if-then form, the "if" part contains the hypothesis and the "then" part. ontains the conclusion.
Identify the hypothesis and conclusion of the conditional: If a triangle is a right triangle, then it has 90° angle . Answer: Hypothesis: a triangle is a right triangle. Conclusion: it has a 90° angle. Show the conditional is false by finding a counterexample: If it is an animal, then it has four legs.
This concept teaches students to rewrite statements in if-then form and determine the hypothesis and conclusion. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic.
Hypothesis: "It rains." Conclusion: "I'll bring an umbrella." Example 2. Determine the hypothesis and conclusion: All right angles are 90 ∘. Hypothesis: "An angle is right." Conclusion: "It is 90 ∘." Example 3. Use the statement: I will graduate when I pass Calculus. Rewrite in if-then form and determine the hypothesis and conclusion.
same thing as 'I get what I like'!". "You might just as well say," added the Dormouse, who seemed to be talking in his sleep, "that 'I breathe when I sleep' is the same thing as 'I sleep when I breathe'!". "It is the same thing with you," said the Hatter, and here the conversation dropped, and the party sat silent for a minute.
conclusion, q. Determining Whether a Statement Is True or False. Work with a partner. A hypothesis can either be true or false. The same is true of a conclusion. For a conditional statement to be true, the hypothesis and conclusion do not necessarily both have to be true. Determine whether each conditional statement is true or false.
Hypotheses followed by a conclusion is called an If-then statement or a conditional statement. This is noted as. p → q p → q. This is read - if p then q. A conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said "if you get good grades then you will not get into a good ...
Math Background The truth value of a conditional statement is a function of the truth values of its hypothesis and its conclusion. The only way a conditional can be false is if its hypothesis is true and its conclusion is false. This fact forms the basis for using a counterexample to disprove a conjecture. More Math Background: p. 78C Lesson ...
Geometry Ch 2 HW Packet: Segments 2.5 Worksheet Name_____ For #1 - 3, identify the Hypothesis and Conclusion for each conditional statement. 1) If Corrine saves up $500, then she is going to buy a season pass to Disneyland.
Example. Conditional Statement: "If today is Wednesday, then yesterday was Tuesday.". Hypothesis: "If today is Wednesday" so our conclusion must follow "Then yesterday was Tuesday.". So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states. Converse: "If yesterday was Tuesday, then ...
2.1-2.3 WS Conditionals - Free download as Word Doc (.doc), PDF File (.pdf), Text File (.txt) or read online for free. This document provides a geometry worksheet with questions about conditionals. It includes questions about writing the hypothesis and conclusion of conditional statements, writing the conclusion of syllogisms, writing conditionals from given hypotheses and conclusions ...
This document contains an activity sheet for mathematics students in grade 8. The activity sheet focuses on if-then statements, including determining the relationship between hypotheses and conclusions, transforming statements into equivalent if-then statements, and matching hypotheses and conclusions. The activity sheet provides 3 activities for students to practice these skills along with ...
The converse is formed by exchanging the hypothesis and conclusion of the conditional. Converse: If a number is an integer , then it is a whole number. False; Sample answer: ± The inverse is formed by negating both the hypothesis and conclusion of the conditional. Inverse: If a number is not a whole number , then it is not an integer.
Geometry: 2 - 2 Conditionals Worksheet Name _____ I. State the hypothesis and conclusion for each statement. 1. If you are funny, then you will make people laugh. 2. If a point is in the interior of an angle, then it cannot be in its exterior. 3. If A is between B and C, then A, B, and C are collinear. II.
So, using the if- then statement, the input is the hypothesis of the statement and the output is the conclusion of the statement. Answer: If I studied for my math test, then I got a good grade. 2. Input: It is raining. Output: We need to use our umbrella. So, using the if- then statement, the input is the hypothesis of the statement
For the following problems, underline the hypothesis and highlight the conclusion in each conditional statement. 1. If today is Monday, then tomorrow is Tuesday. 2. If a truck weighs 2 tons, then it weighs 4000 pounds. Write each statement in if-then form. 3. All chimpanzees love bananas. 4. Collinear points lie on the same line.
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