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Consider rolling a six-sided die. Let A be the set of
Chapter , Problem 1(choose chapter or problem)
Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number. Let B be the set of outcomes where the roll is greater than 3. Calculate and compare the sets on both sides of De Morgan's laws.
\((A \cup B)^{c}=A^{c} \cap B^{c} . \quad(A \cap B)^{c}=A^{c} \cup B^{c}.\)
Questions & Answers
QUESTION:
Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number. Let B be the set of outcomes where the roll is greater than 3. Calculate and compare the sets on both sides of De Morgan's laws.
\((A \cup B)^{c}=A^{c} \cap B^{c} . \quad(A \cap B)^{c}=A^{c} \cup B^{c}.\)
ANSWER:Step 1 of 3
Let S be the sample space of rolling a die.
\(S=\{1,2,3,4,5,6\}\)
Let A be the set of outcomes where the roll is an even number.
\(A=\{2,4,6\}\)
\(A^{c}=\{1,3,5\}\)
Let B be the set of outcomes where the roll is greater than 3
\(B=\{4,5,6\}\)
\(B^{c}=\{1,2,3\}\)