Question

Let A, B, C be sets such that A ∩ B ≠ ϕ, B ∩ C ≠ ϕ and A ∩ C ≠ ϕ. Do you claim that

A ∩ B ∩ C ≠ ϕ ? Justify your answer. ​

Answer 1

Answer:

but why will u tell me pgal ???

who are you to tell me pgal ...

any prime minister ...

Answer 2

Step-by-step explanation:

Given that:-

Let A, B, C be sets

given that A ∩ B ≠ ϕ,

Clearly both A and B are non empty they have common elements.

B ∩ C ≠ ϕ It is clear that B and C are non empty they have common elements

A ∩ C ≠ ϕ it is clear that A and C are non empty

they have common elements

So we conclude that

A,B,C are non empty sets

A ∩ B ∩ C ≠ ϕ is also non empty set

Let consider

A={1,2} B={2,3}, C={2,3,4}

A ∩ B={1,2}∩{2,3}={2}

B ∩ C ={2,3}∩{2,3,4}={2,3}

A ∩ C={1,2} ∩ {2,3,4}={2}

Now (A ∩ B) ∩ C={2}∩{{2,3,4}={2}≠ϕ