AssumeOriginally Posted by gryphon_gold
and is false. Then, be de Morgan laws.
If,
then
Then,
Contradiction,
Thus,
Problem:
If S x T = U x V, then show that S = U and T = V.
Incomplete Solution:
Step 1) S x T = {(a,b) | a e S, b e T}; U x V = {(c,d) | c e U, d e V}
Step 2) {(a,b) | a e S, b e T} = {(c,d) | c e U, d e V}
.
.
.
Step n-1) a = c for all a e S, c e U; b = d for all b e T, d e V
Step n) S = U; T = V
Question: How do I make a formal connection between steps 2 and N-1?