- #1
SpY]
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At first glance these things seem so intuitive and familiar from other maths (like distribution) that I don't see how/where to start in proving them; while I know its probably quite simple. I understand what union and intersection are, but I'm unsure if multiplying two sets means a new set with elements being every permutation between the two sets.
Trichotomy - [tex]A \subseteq B , B \subseteq C then A \subseteq C[/tex]
For non empty sets, [tex]A \times (B \cap C) = (A \times B) \cap (A \times C)[/tex]
[tex](A \times B) \cap (A\timesB) = (A \cap B) \times (A \cap B)[/tex]
Trichotomy - [tex]A \subseteq B , B \subseteq C then A \subseteq C[/tex]
For non empty sets, [tex]A \times (B \cap C) = (A \times B) \cap (A \times C)[/tex]
[tex](A \times B) \cap (A\timesB) = (A \cap B) \times (A \cap B)[/tex]