Showing top 8 worksheets in the category converse inverse contrapositive. Converse statement inverse statement contrapositive statement of the sales pitch of each ad. Converses, contrapositives and proof by the contrapositive. However, the contrapositive of a true conditional is always true, and the contrapositive of a false conditional is always false. You will also learn how to determine whether or not a statement is biconditional. Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. If two segments are congruent, then they have the same length. Variations on the conditional statement direct statement converse inverse contrapositive if p, then q. Ixl converses, inverses, and contrapositives geometry. Statements which always have the same truth values are logical equivalents. Determining that conditional and contrapositive are. Conditional statements converse inverse contrapositive truth value counter example you will receive a worksheet as well as fill in the blank notes with the purchase of this resource.
Write both the converse and the contrapositive of the conditional statement below. In classical logic, an implication is logically equivalent to its contrapositive, and, moreover, its inverse is logically equivalent to its converse. Worksheets are unit 4 logic packet, logic and conditional statements, lesson practice a conditional statements, conditional statements, geometry, geometry, converse and contrapositive work 3. The definition of a triangle is, a closed figure with three straight sides and three angles. If a polygon is not regular, then it is not equilateral. Logic and proof converse, inverse, and contrapositive.
Conditional converse inverse contrapositive worksheets. Jacob wigfields answer is quite right and his example is very helpful. If you do not have a sprite, then you do not have a root beer. Determine if each resulting statement is true or false. Converse, inverse, and contrapositive statements read. Some of the worksheets displayed are converse and contrapositive work 3, inverse converse contrapositive and, logic and conditional statements, lesson practice a conditional statements, geometry notes inductive reasoning conditional, unit 4 logic packet, geometry work using. This is because it is easier to transforminformationabout xintoinformationabout7.
If a polygon is not equilateral, then it is not regular. Converse, inverse, and contrapositive if a given conditional statement is true, the converse and inverse are not necessarily true. Vocabulary organizer, suggested learning strategies. Statements with the same truth values are logically equivalent. The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional. For every conditional statement you can write three related statements, the converse, the inverse, and the contrapositive. What are the differences between inverse, converse, and. Contrapositive, converse, inverse words that made you tremble in high school geometry.
How do you write the converse, inverse, and contrapositive. Converse inverse contrapositive worksheets teacher. The converse of the implication p q is the reverse implication q p. Conditionals and contrapositives are logical equivalents, and inverses and converses are logical equivalents. This lesson targets the converse, inverse, contrapositive of a conditional and then introduces biconditionals in the study of logic. Also, the converse of a statement is logically equivalent to the inverse of the statement. The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit. Displaying all worksheets related to conditional converse inverse contrapositive. Sophie alpert on converse, inverse, and contrapositive. Converse, inverse, and contrapositive learning targets. For one of the ads, demonstrate the laws of syllogism and detachment. If a number is divisible by 2, then it is divisible by 4. Converse, inverse, and contrapositive find the converse, inverse, and contrapositive. If the sum of two angle measures is 90, then they are complementary.
Create additional stanzas using related if, then statements. How do you write the converse, inverse, and contrapositive of a conditional statement and determine their truth values. When two statements are both true or both false, we say that they are logically equivalent. The converse of a statement is simply taking the variables in the statement and switching their place. The inverse is formed by negating the hypothesis and negating the conclusion. We will now discuss converse, inverse, and contrapositive statements. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement. That is, we can determine if they are true or false.
This lesson will help you with ideas for teaching these statements and their alternate forms. Write a true conditional statement whose inverse is false. It can be modified to only focus on converse, inverse, contrapositive or just biconditionals. Finally, if you negate everything and flip p and q taking the inverse of the converse, if youre fond of wordplay then you get the contrapositive. It is very important to realize that these two implications are not logically equivalent. Converse, inverse, and contrapositive on exercise topics. If its not the broncos, then the helmet is not orange and blue. A contrapositive statement is formed by negating both the hypothesis and conclusion, and switching them.
Use the law of detachment to reach a logical conclusion about the following statement. If the original statement and the converse are true, how can it be written as. Now if you take a second to think about that, thats true. I think students will quickly realize not to do that whether we tell them or not and it seems to make adding detailed sentencespecific hints a. A conditional statement and its contrapositive are logically equivalent. First, change the statement into an ifthen statement.
Converse, inverse, and contrapositive examples video. What are the converse, contrapositive, and inverse. The inverse and converse in logic are two ways of rewriting a statement with predefined structures. Contrapositive formed by negating the hypothesis and conclusion of the converse. Again in symbols, the contrapositive of p q is the statement not q not p, or q p. The first is a conditional statement, and the second could be its converse, inverse, or contrapositive. It is not possible to determine whether or not the converse and inverse of a statement are true if all you have is knowledge of the original statement, although if either the converse or inverse of a statement is true, the other is true as well. The conditional statement, inverse, converse and contrapositive all have a truth value. Write the converse, the inverse, and the contrapositive of the conditional statement. Determine whether each related conditional is true or false.
Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Investigating advertising slogans using conditional. If you run a red light, then you are breaking a traffic law. Moveable gray and white boxes reveal key information. These new conditionals are called the inverse, converse, and contrapositive. I only offer a bit of clarification and some precision. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Remote work advice from the largest allremote company. Cut the boxes apart and sort them into a converse group, an inverse group, and a contrapositive group. A conditional statement is logically equivalent to its contrapositive. Unit 4 logic packet humble independent school district. Asked in calculus, definitions, geometry what is converse inverse and contrapositive.
The statement \a implies b can be written symbolically. Finally, determine if the inverse, converse, and contrapositive are true or false and determine if the advertisement was realistic. Chapter 3 introducing the contrapositive and converse in the last chapter see theorem 2. Chapter 3 introducing the contrapositive and converse. Environmental education resources to commemorate earth days 50th anniversary. Likewise, the converse and inverse of a conditional are either both true or both false. Find the converse, inverse, and contrapositive of conditional statements. Interactive word wall, thinkpairshare, group presentation, discussion groups. These sound hard but are actually quite easy once you memorize what they are.
Converse, inverse, and contrapositive were going to look at these three terms using this statement, if something is a dog, then it is a mammal. For any conditional statement there are several other similarsounding conditional statements. The negation of a statement simply involves the insertion of the word not at the proper part of the statement. The contrapositive of a conditional statement of the form p. Here youll learn how to find the converse, inverse and contrapositive of a conditional statement. Write the converse, inverse, and contrapositive of the statement all squares are rectangles. Improve your math knowledge with free questions in converses, inverses, and contrapositives and thousands of other math skills.