Set Theory Results

Consider A,B and C are the sets, then

1. A \subseteq A \cup B and B \subseteq A \cup B

2. A \cup \emptyset  = A

3. A \cap \emptyset = \emptyset

4. A \subseteq C and B \subseteq C then A \cup B \subseteq C

5. A \subset B if and only if A \cup B = B

6. A \subset B if and only if A \cap B = A

7. A \cap B \subseteq A and A \cap B \subseteq B

8. If A \subseteq B and A \subseteq C then A \subseteq B \cap C

9. A \cap U = A

10.A \cup U = U

11.{({A^C})^C} = A

12.{\emptyset ^C} = U and {U^C} = \emptyset

13.A \cup {A^C} = U

14. A \cap {A^C} = \emptyset

15. If A \subseteq B then {B^C} \subseteq {A^C}

16. If  x \in A and x \in B then x \in A \cap B

17. If x \in A or x \in B then x \in A \cup B

18. A - B = A \cap {B^C}

19. A - (A - B) = A \cap B

20. A - (A - B) = A - (A \cap {B^C})

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