Respuesta :
Here's a counterexample: let
[tex] B = \{1, 2, 3, 4, 5\},\quad D = \{A, B, C, D, 5\}[/tex]
We choose the subsets as follows:
[tex]A = \{1, 5\},\quad C = \{A, B, C\}[/tex]
It is true that [tex]A\subseteq B[/tex] and [tex]C\subseteq D[/tex] and that [tex]A\cap C=\emptyset[/tex], but [tex]A\cap D = \{5\}[/tex]
From the sample sets I used, I have given a counterexample to the assertion that A and D have no elements in common because it was proven that;
A ∩ C = Ø
A ∩ D = {5}
- This is about sets notation.
We are told that there are 4 sets namely; A, B, C & D.
We are told that; A ⊆ B and C ⊆ D.
The symbol ⊆ means Subset.
Therefore set A is a subset of set B and set C is a subset of set D.
- Now, we are told that those 4 given sets are subsets in such a way that set A and set C have no elements in common. We want to refute the theory that Set A and set D have no elements in common.
- Let's give some set example as;
Set A = {1, 2, 5}
Set B = {1, 2, 3, 4, 5}
Set C = {6, 7, 8}
Set D = {5, 6, 7, 8, 9}
- From these sample sets, we can see that;
A ∩ C = Ø
However, A ∩ D = {5}
- Since we have proved that A and D have elements in common, it means we have been able to give a counterexample to the assertion that A and D have no elements in common.
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