The operation intersection on sets has an identity? True or False?Justify the answer by giving proofs or example

james2011 | Student

The identity for set intersection operation is the whole set.

Let S be the whole set, and A any subset of S, we will have

S∩A = A∩S = S

Therefore S is the identity.

giorgiana1976 | Student

The intersection of two sets is also a set that comprises all common elements to both sets.

We can state this assumption using logical connectors, as it follows:

x belongs to the set A∩B,if and only if x belongs to A  ^ x belongs to B. The logical connector "^" represents a conjunction and it could be replaced by the word "and".

We'll analyze the intersection between the sets A = {1,3,5} and B = {3,5,7}.

A∩B = {1,3,5}∩{3,5,7}

The common elements to A and B are those elements that are in A and they are in B, too: {3,5}

A∩B = {3,5}

When two or more sets have no common elements, they are disjoint and the result of intersection is the empty set.