Question

Find sets A, B and C such that \[A \cap B,\] \[B \cap C\] and \[A \cap C\] are non-empty sets and \[A \cap B \cap C = \phi \].

Answer 1

Hint:
Here we can let any of the three sets satisfying the above condition and so from there we can prove whether the sets satisfying above condition is true or not and hence we can obtain our required answer.

Complete step by step solution:
As given that \[A \cap B,\] \[B \cap C\] and \[A \cap C\] are non-empty sets and \[A \cap B \cap C = \phi \]
Let the random set be as \[A = \{ 0,1\} ,B = \{ 1,2\} ,C = \{ 2,0\} \]
Now, calculating the above we get,
As obtaining the intersection of terms two terms simultaneously, we get,
\[A \cap B = \{ 1\} \]
Again for another term we get,
\[B \cap C = \{ 2\} \]
And similarly for the last term we get,
\[A \cap C = \{ 0\} .\]
And hence above taken sets are in such a way that it satisfies the condition of \[A \cap B \cap C = \phi \]

Hence, set A, B and C are found satisfying the above condition.

Note:
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. ... The intersection of two sets is a new set that contains all of the elements that are in both sets. The above question can also be proceeded with the Venn diagram. And let the set in such a way that it satisfies the above condition.