Intersection of Connected Sets: True or False?

[beetle2]

I have been asked if the following is true or false

the intersection of two connected sets is connected ?

I would have thought that if their intersection was empty they wouldn't be connected.

If they were disjoint or course it would be empty.


any ideas?

 

[lavinia]

there are simple counter examples

 

[Office_Shredder]

The empty set definitely is connected. Take a look at the definition of not connected again... the partioning sets are required to be non-empty themselves (otherwise every set is disconnected). The empty set has no non-empty subsets so must be connected by default

 

[beetle2]

So are you saying that if I take two non empty connected sets ie.

A= {1} and B={2} as singletons are connected then the intersection of (A n B ) = the empty set which is itself connected?

 

[beetle2]

So I need to find at least an non empty set to be dissconnected.

 

[lavinia]

So are you saying that if I take two non empty connected sets ie.

A= {1} and B={2} as singletons are connected then the intersection of (A n B ) = the empty set which is itself connected?

he is saying that the empty set is connected so that it will not serve for a counter example

 

[beetle2]

Thanks guys

 

[Jamma]

Just try to imagine two connected sets that cross over each other in two disconnected regions; it's not too difficult if you think about it e.g. take two connected subsets of a circle which cover the circle but are not the whole circle.