What is the complement of a product of two sets? I am given this information: > Suppose $A=\\{1,2,3\\}$, $B=\\{3,5\\}$, $C=\\{1,2,4,6,9\\}$ and $U = \\{0, 1, 2, 3, 4, 5, 6,7,8,9\\}$. Enter "T" for each true, and "F" for each false statements. There are problems like $|(A \times B)'| = 94$. I _think_ this is false, because: $A \times B$ produces a set of tuples. The absolute complement of a set $S$ is the set of all elements of $U$ that are not elements in the set $S$. There are no tuples in $U$, so $A \times B$ has none of the elements of $U$, therefore, $(A \times B)'$ should produce the set $U$. If this thinking is true, then $|(A \times B)'| = 10$ Have I missed something/is my thinking correct?

In my opinion your reasoning is almost correct as it is never stated the universal set for ordered pairs is $U \times U$.

$A \times B \
ot \subset U$ so $(A \times B)'$ is a meaningless statement and the question makes no sense.

In my opinion.

However it is obviously the intended case that the universal set for ordered pairs is intended $U \times U$.

$|U \times U| = 10*10 = 10$

$|A \times B| = 2*3 = 6$ so $|(A \times B)'|=94$.

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I say "Phooey on everything".