Quite often in this course, you will need to analyze general statements, including conjectures about groups of things that may be alike in some ways and different in others. Venn diagrams are perfect for organizing your thoughts about differences and similarities among items, but it takes practice to learn how to create and read these graphic tools. Consider the situation below, which leads a student named Noah to create several claims, or conjectures, that will need to be tested. 

To help him sort out his plans, Noah has created the Venn diagram below.

Which of Noah's conjectures are supported by the Venn diagram above? Read each of the claims below. When you think you know if the conjecture is supported by the diagram, click the Show Me button to check your work.

Eleven of my friends would like to go hiking.	This statement is supported by the Venn diagram. There are 7 friends who would like to go hiking, and 4 who would hike or swim. That means there are a total of 11 friends who would like to go hiking.
At least 10 of my friends would like to go swimming.	This conjecture is supported by the Venn diagram. While only 9 friends prefer swimming, there are 4 more who would enjoy hiking or swimming. Therefore, a total of 13 people are interested in swimming. That's more than 10.
Seven of my friends would not like to go swimming.	The conjecture that 7 of Noah's friends do not want to go swimming is not supported by the diagram. Seven friends would prefer to go hiking, but there is also a friend who doesn't want to swim or hike. All together, there are 8--not 7--friends who do not want to go swimming.
More people prefer swimming than hiking.	This conjecture is supported. Nine of Noah's friends would like to go swimming while only 7 would like to go hiking.

Now try testing some conjectures on your own, using the activity below. Click the Activity button to access the Venn diagram worksheet. When you've completed the worksheet, click on the Answer Key button to check your work.