Conditionals and Euler diagrams
A conditional statement is an “if-then” statement
In this lesson we’ll look at how to write conditional statements and how to draw and interpret Euler diagrams.
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Conditional statement
A conditional statement is an if/then statement where the “if” part is the hypothesis and comes first, and the “then” part is the conclusion and comes second.
You always write a conditional statement like this:
“If ???A???, then ???B???.”
This kind of conditional statement tells you that, if ???A??? is true, then ???B??? must be true also.
How to build Euler diagrams from conditional statements
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Rewriting statements as conditionals
Example
Write the statement as a conditional statement.
“All dogs have fur.”
We need to create a hypotheses and a conclusion from the statement “All dogs have fur.”, and write it as an if/then statement. In this statement, the hypothesis is “It’s a dog” and the conclusion is “it has fur”. This makes the conditional statement
“If it’s a dog, then it has fur.”
Because we were told that all dogs have fur, we know that if something is a dog, then it must have fur.
A conditional statement is an if/then statement where the “if” part is the hypothesis and comes first, and the “then” part is the conclusion and comes second.
Euler diagrams
An Euler diagram shows the exact relationship described in a conditional statement. It’s different from a Venn Diagram, because a Venn Diagram would show all of the possibilities, including the ones not described in the conditional statement.
They are often of the form:
“If ???A???, then ???B???.”
“If ???A???, then not ???B???.”
Let’s look at an example.
Example
What is the conditional statement represented in the Euler diagram?
The diagram has the form “If ???A???, then ???B???.”
So we replace ???A??? and ???B??? with the values from the diagram, and we write
“If it’s a cat, then it’s a mammal.”
Let’s tie both ideas together.
Example
Write the following statement as a conditional statement and draw the matching Euler diagram.
“I get my allowance when I do my homework.”
Let’s think about what comes first in the statement. First the homework gets done, then there’s an allowance. This makes the conditional statement
“If I do my homework, then I get my allowance.”
???A??? is the homework, and ???B??? is the allowance, which makes the Euler diagram
