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How do you prove W ⊆ V?

User Kissed
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Final answer:

To prove W ⊆ V, you must show that every element of W is also an element of V. For the Venn diagram, draw two intersecting circles for events C and P, with the overlap showing elements common to both C and P, namely {blue}, and the union showing all elements in C or P.

Step-by-step explanation:

To answer the question on how to prove W ⊆ V (W is a subset of V), you would need to demonstrate that every element in set W is also an element of set V. However, the student's question also involves drawing a Venn diagram for a probability experiment. Let's tackle both aspects separately:

Proving a Subset

To prove W ⊆ V, you assume that you have an arbitrary element, say x, in set W. Then, you show that this x is also in set V. If you can do this for every element in W, then W is a subset of V.

Venn Diagram for Probability

Constructing a Venn diagram for the provided experiment, we can visualize two events C and P. Event C includes {green, blue, purple} and event P includes {red, yellow, blue}. In the diagram, the space where C and P overlap would contain {blue} to represent C AND P, and the union of both C and P would be {green, blue, purple, red, yellow} to represent C OR P.

User Benjamin Jimenez
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