Check all true statements.
1) If A={1,2} and B={3} then A x B ={ {1,3}, {2,3} }. 2) The

cartesian product is symmetric, i.e. A x B = B x A for all sets A,B.

3) The cartesian product is associative, i.e. (A x B) x C = A x (B x C) = for all sets A,B,C. Both sets are equal to A x B x C.

4) If A x B = C x D, and none of these sets are empty, then A=C and B=D.

5) If A={1,2} and B={3} then A x B ={ (1,3), (2,3) }. 

6) The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A,B,C and A nonempty, then B = C.

7) The cardinality of A x B is the sum of the cardinalities of A and B.

8) The cartesian product has a cancellation property, i.e. if A x B = A x C for some sets A,B,C, then B = C.

9) The power set of the cartesian product of A and B is the cartesian product of the power sets of A and B.

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