Discrete math prove setsI am wondering if my answer to this problem is correct.Statement: ∀...

Ethen Blackwell

Ethen Blackwell

Answered

2022-07-15

Discrete math prove sets
I am wondering if my answer to this problem is correct.
Statement: A , B , C : [ A B C ] [ C × B B × A ] [ A = B = C ].
Question: is the above statement true or false?
Answer: true.
Proof: x B × A   a n d   x C × B for some a A   a n d   b B which gives us a A B C a B and a C also we get b B C b C så we get x = ( a , b ) C × B and x B × A.
Is this proof enough or even correct?
Can someone tell me if I'm right or wrong?

Answer & Explanation

Dominique Ferrell

Dominique Ferrell

Expert

2022-07-16Added 18 answers

Step 1
The statement is not true.
If A = B = then the conditions are satisfied for every set C.
The statement is true under the extra condition that B .
Let it be that b 0 B.
If c C then c , b 0 C × B B × A and we conclude that c B.
Step 2
Proved is now that C B and combining this with B C we conclude that B = C.
If b B then b C (see above) so b , b C × B B × A and we conclude that b A.
Proved is now that B A and combining this with A B we conclude that A = B.

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