Is it correct to say AX A= {(a, a) : a belongs to A}?
- John-Michael Kuczynski
- Dec 19, 2020
- 1 min read
No.
A X A= { <x,y>: x e A & y e A}
Explanation: A X B = { <x,y>: x e A & y e B}
In other words, A X B is the class of all ordered pairs <x,y> such that x belongs to A and b belongs to B.
Therefore, A X A= { <x,y>: x e A & y e A}
What you wrote is syntactically ill-formed, and it’s suggested meaning is false, since no set contains every ordered pair consisting of its own members.
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