Binary relation in a cartesian product

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The discussion centers on determining the number of binary relations that can be formed from the Cartesian product of sets A = {1, 2} and B = {a}. It is established that there are two ordered pairs in the Cartesian product A * B, leading to a total of four possible binary relations. The user expresses confusion about the specific relations, initially listing them incorrectly. Clarification is provided that valid binary relations include the empty set, individual pairs, and combinations of pairs. The conversation emphasizes the importance of understanding how binary relations are derived from Cartesian products.
nafees ahmad
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How many binary relation can be formed from the cartesian product below:
A = { 1 , 2 } & B = {a }
i know there are two ordered pairs in this cartesian products A * B.
i also know that there are 4 binary realtions. could someone please write
those four relations for me, i am really confused here.
 
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{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.
 
HallsofIvy said:
{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.

I'd imagine, they're actually something more like these: {}, {(1, a)}, {(2, a)}, and {(1, a), (2, a)}...
 
thanx. i really apprecite u for this
 

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