Question #302386




Consider the following sets.


U = { 1, 2, …. 10 }


A = { 3, 4, 5, 6, 8, 10 } ` C = { 2, 4, 6, 7, 8 }


B = { 1, 3, 5 }


Perform the following set operations by writing the resulting sets using the roster method. Moreover, sketch the Venn diagram.


1. A’ = ________________________________________________

2.B’ = ________________________________________________

3. A U B = _____________________________________________

4. A ∩ B = _____________________________________________

5. A' ∩ B = _____________________________________________

6. (A ∩ B) U C = _________________________________________

7. A ∩ (B U C’) = _________________________________________


1
Expert's answer
2022-02-25T12:33:53-0500

1. A={1,2,7,9}A' = \{1,2,7,9\}



2. B={2,4,6,7,8,9,10}B' = \{2,4,6,7,8,9,10\}



3. AB={1,3,4,5,6,8,10}A \cup B = \{1,3,4,5,6,8,10\}



4. AB={3,5}A \cap B = \{3,5\}



5. AB={1}A'\cap B = \{1\}



6. (AB)C={2,3,4,5,6,7,8}(A\cap B)\cup C = \{2,3,4,5,6,7,8\}



7. A(BC)={3,5,10}A \cap (B\cup C') = \{3,5,10\}


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