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#### bergausstein

##### Active member

- Jul 30, 2013

- 191

just want to know if my answers are correct.

1. for any set A, a set of subsets of A is said to be exhaustive if the union of these subsets is A, and is said to be disjoint if no two of the subsets have any element in common. if $\displaystyle A\,=\,\{a,\,b,\,\,c\},\,$ tell whether the following set of subsets is exhaustive;disjoint.

a. $\{a\},\,\{b\}$ - disjoint

b. $\{a\},\,\{b,c\}$ - exhaustive and disjoint

c. $\{a,b\},\,\{b,c\}$ - exhaustive

d. $\{a\},\,\{a,b\}$ - neither

e. $\{a\},\,\{b\},\,\{c\}$ - exhaustive and disjoint

2. Tell under what conditions on the sets A and B we would have each of the following:

a. $\displaystyle A\cap B\,=\,\emptyset$ - if A & B are disjoint

b. $\displaystyle A\cap B\,=\,U$ - if both A & B are $\emptyset'$

c. $\displaystyle A\cup B\,=\,U$ - if A or B is $\emptyset'$

d. $\displaystyle A\cup B\,=\,\emptyset$ - if both A and B are $\emptyset$

e. $\displaystyle A\cap U\,=\,A$ - if $A\subset B$

f. $\displaystyle A\cup B\,=\,A$ -if $B\subset A$

g. $\displaystyle A\cap \emptyset\,=\,\emptyset$ - if A is $\emptyset$

h. $\displaystyle A\cap U\,=\,A$ - if A is $\emptyset$

i. $\displaystyle A\cup U\,=\,U$ - if $A\subset B$

j. $\displaystyle A\cup U\,=\,A$ - if A is $\emptyset$

k. $\displaystyle A\cup \emptyset\,=\,U$ - if A is $\emptyset'$

l. $\displaystyle A\cup\emptyset\,=\,\emptyset$ - if A is $\emptyset$

please tell me where I'm wrong and teach me how to approach that problem properly. thanks!

1. for any set A, a set of subsets of A is said to be exhaustive if the union of these subsets is A, and is said to be disjoint if no two of the subsets have any element in common. if $\displaystyle A\,=\,\{a,\,b,\,\,c\},\,$ tell whether the following set of subsets is exhaustive;disjoint.

a. $\{a\},\,\{b\}$ - disjoint

b. $\{a\},\,\{b,c\}$ - exhaustive and disjoint

c. $\{a,b\},\,\{b,c\}$ - exhaustive

d. $\{a\},\,\{a,b\}$ - neither

e. $\{a\},\,\{b\},\,\{c\}$ - exhaustive and disjoint

2. Tell under what conditions on the sets A and B we would have each of the following:

a. $\displaystyle A\cap B\,=\,\emptyset$ - if A & B are disjoint

b. $\displaystyle A\cap B\,=\,U$ - if both A & B are $\emptyset'$

c. $\displaystyle A\cup B\,=\,U$ - if A or B is $\emptyset'$

d. $\displaystyle A\cup B\,=\,\emptyset$ - if both A and B are $\emptyset$

e. $\displaystyle A\cap U\,=\,A$ - if $A\subset B$

f. $\displaystyle A\cup B\,=\,A$ -if $B\subset A$

g. $\displaystyle A\cap \emptyset\,=\,\emptyset$ - if A is $\emptyset$

h. $\displaystyle A\cap U\,=\,A$ - if A is $\emptyset$

i. $\displaystyle A\cup U\,=\,U$ - if $A\subset B$

j. $\displaystyle A\cup U\,=\,A$ - if A is $\emptyset$

k. $\displaystyle A\cup \emptyset\,=\,U$ - if A is $\emptyset'$

l. $\displaystyle A\cup\emptyset\,=\,\emptyset$ - if A is $\emptyset$

please tell me where I'm wrong and teach me how to approach that problem properly. thanks!

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