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Video: Determining the Universal Set given Two Sets in Word Problems

Bethani Gasparine

If 𝑋 is the set of math teachers in a school and 𝑌 is the set of science teachers in the school, what could be the universal set that contains 𝑋 and 𝑌?

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Video Transcript

If 𝑋 is the set of math teachers in a school and π‘Œ is the set of science teachers in the school, what could be the universal set that contains 𝑋 and π‘Œ?

The universal set 𝑒. The universal set is a set containing all elements and of which all other sets are subsets, meaning they’re within the universal set. So 𝑋 is the set of math teachers. And π‘Œ is the set of science teachers. So where could both of these teachers belong?

Here’s a Venn diagram to represent the set 𝑋 and π‘Œ, the math teachers and the science teachers. And there may be a few teachers who teach math and science. So- so what could be the universal set that holds all of this? It would need to be all of the teachers in the school because the math teachers would be a subset of all of the teachers and the science teachers would be a subset of all of the teachers. Therefore, 𝑒 is the set of all teachers.