Calculate and compare the sets on both sides of De Morgan’s laws.

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admin 166 2021年4月12日 0条评论

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

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admin · Answer 1 · 2021-04-12T16:00:09+00:00

We have
$A=\{2,4,6\}, \quad B=\{4,5,6\},$
so $A \cup B=\{2,4,5,6\}$ , and
$(A \cup B)^{c}=\{1,3\} .$
On the other hand,
$A^{c} \cap B^{c}=\{1,3,5\} \cap\{1,2,3\}=\{1,3\}$
Similarly, we have $A \cap B=\{4,6\}$ , and
$(A \cap B)^{c}=\{1,2,3,5\}$
On the other hand,
$A^{c} \cup B^{c}=\{1,3,5\} \cup\{1,2,3\}=\{1,2,3,5\}$

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Calculate and compare the sets on both sides of De Morgan’s laws.

Published by admin on 2021年4月12日

1 答案