Conditional statements are all part of logic. Conditional statements are also called 'if-then' statements. A conditional statement can be written in the form, "If is the**p****hypothesis**of the statementis the**q****conclusion**of the statement
Sometimes a graphic can make things clearer. |
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If a conditional statement is true, the conclusion is always true when the hypothesis is true. Can you see why this is the case? The Venn Diagram shows the relationship between - The
is the part that follows the*hypothesis*or the**p****if** - The
is the part that follows the**conclusion**or the**q****then**
We can take a look at it with some statements in the Venn and that may make it even clearer! Let's take a look at this example… |
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Here's our conditional statement, "If a fruit is a banana, then it grows on a tree." - hypothesis (
): bananas are a fruit**p** - conclusion (
): they grow on a tree**q**
The Venn Diagram shows clearly that all bananas are fruits that grow on trees. In math 'terms,' you can write this as |
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and, this is read, "If |
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Now, you may be wondering how to write the |
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and, this is read, "If |
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In this case, the converse of the statement is, "If it grows on a tree, then the fruit is a banana." Get it? Just flip the conclusion and the hypothesis around! It's that easy! What if the conditional statement was, "If a dog is a Dachshund, then it is a wiener dog." The converse would be, "If a dog is a wiener dog, then it is a Dachshund." |
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How about the |
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This is read, "If not |
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So the The wiener dog conditional statement, "If a dog is a Dachshund, then it is a wiener dog" becomes "If a dog is not a Dachshund, then it is not a wiener dog." |
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How do you write the |
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This is read, "If not |
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Can you figure out what the contrapositive of our banana statement would be? Did you say, "If it doesn't grow on a tree, then it isn't a banana?" If you did, well then, you are correct! Yahooo! |
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©2016 Sherry Skipper Spurgeon for Geometry Bugs Me All Rights Reserved |
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