3.1.1.1: Exercises

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List the elements of the set “The letters of the word Mississipi”
List the elements of the set “Months of the year”
Use a word description, and set-builder notation for the set \(\{3,6,9\}\)
Use a word description, and set-builder notation for the set \(\{a, i, e, o, u\}\)
Is \(\{1,3,5,6\}\) a subset of the set of odd integers?
Is \(\{A, B, C\}\)a subset of the set of letters of the alphabet?
Consider the sets below, and indicate if each statement is true or false.
\(A=\{1,2,3,4,5\} \quad B=\{1,3,5\} \quad C=\{4,6\} \quad U=\{\text {whole numbers from } 0 \text { to } 10\}\)
1. \(3 \in B\)
2. \(5 \in C\)
3. \(B \subset A\)
4. \(C \subset A\)
5. \(C \subset B\)
6. \(C \subset U\)
Use the sets from above and treat \(U\) as the Universal set. Find each of the following:
1. \(A \cup B\)
2. \(A \cup C\)
3. \(A \cap C\)
4. \(B \cap C\)
5. \(A^{c}\)
6. \(B^{c}\)
Let \(D=\{b, a, c, k\}, \quad E=\{t, a, s, k\}, \quad F=\{b, a, t, h\}\). Using these sets, find the following:
1. \(D^{c} \cap E\)
2. \(F^{c} \cap D\)
3. \((D \cap E) \cup F\)
4. \(D \cap(E \cup P)\)
5. \((F \cap E)^{c} \cap D\)
6. \((D \cup E)^{c} \cap F\)