Consider rolling a six-sided die. Let A be the set of

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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.

\((A \cup B)^{c}=A^{c} \cap B^{c} . \quad(A \cap B)^{c}=A^{c} \cup B^{c}.\)

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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

\(B=\{4,5,6\}\)

\(B^{c}=\{1,2,3\}\)                                                            

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