Question

Prove or disprove the following statements In case you want to prove that they are false, note that for 1, 2 and 3 the negation would start with "there exist sets A,B,C such that...".

1. (1 Point) For all sets A,B and C we have A\(B∪C)=(A\B)∪(A\C).
2. (1 Point) For all sets A,B and C we have If A=B\C, then B=A∪C.
3. (1 Point) For all sets A,B,C,D we have (A×B)∪(C×D)=(A∪C)×(B∪D).

Answer 1

The first and third statements are true, while the second statement is false.

Step-by-step explanation:

To prove or disprove the statements:

1. (1 Point) For all sets A,B and C we have A\(B∪C)=(A\B)∪(A\C).
   The statement is true.
2. (1 Point) For all sets A,B and C we have If A=B\C, then B=A∪C.
   The statement is false.
3. (1 Point) For all sets A,B,C,D we have (A×B)∪(C×D)=(A∪C)×(B∪D).
   The statement is true.