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Chapter 2: Problem 36

Find each of the following sets. \(C \cap \varnothing\)

Short Answer

Expert verified
The intersection of set \(C\) and the empty set is an empty set.

Step by step solution

01

Understand the symbols

Firstly, it's crucial to recognize the symbols used. Here, \(\cap\) represents intersection of two sets. It refers to the common elements between both sets. Also, \(\varnothing\) represents an empty set or a set with no elements in it.
02

Understand set intersection with empty set

The intersection of any set with an empty set results in an empty set itself. That is beacuse empty set doesn't have any element init to be a common one. This property is very handy in set theory and not difficult to memorize.
03

Apply the property

We now know that intersection of any set with the empty set results in empty set. So \(C \cap \varnothing = \varnothing\). This is our result.

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Most popular questions from this chapter

Use the formula for the cardinal number of the union of two sets to solve Exercises 93-96. Set \(A\) contains 30 elements, set \(B\) contains 18 elements, and 5 elements are common to sets \(A\) and \(B\). How many elements are in \(A \cup B\) ?

\(A \cup(B \cap C)=(A \cup B) \cap C\)

Find each of the following sets. \(A \cup \varnothing\)

In Exercises 13-24, let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\\B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \(A \cup(B \cap C)\)

In Exercises 1-12, let $$ \begin{aligned} U &=\\{1,2,3,4,5,6,7\\} \\ A &=\\{1,3,5,7\\} \\ B &=\\{1,2,3\\} \\ C &=\\{2,3,4,5,6\\} . \end{aligned} $$ Find each of the following sets. \(A^{\prime} \cap\left(B \cup C^{r}\right)\)
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