Math

Hello everybody,

According to our textbooks set A is a subset of set B, if and only all the elements of set A are also elements of set B. I am going to take my family as an example. First there were three of us – set A.

A= {Dan, Volha, Serena}

Then Sylver was born and now there are four of us- set B.

B= {Dan, Volha, Serena, Sylver}

Set A is a subset of set B, because all the elements (members of my family) are in set B plus our little one - Sylver.

Is set A a proper set of set B? Set A is a proper set of set B, if and only all the elements of set A are elements of set B and set A is NOT equal set B.

A= {Dan, Volha, Serena}

B= {Dan, Volha, Serena, Sylver}

In my situation set A is a proper set of set B because all elements of set A ( my family members) are in set B, and set B has an extra element ( Sylver ) in it so it makes two sets Not equal to each other, therefore, set A is a proper subset of set B.

The difference between a subset and a proper set that in order to have a proper set two sets cannot be equal to each other that is one of them has to have for at least one extra element.

No set is a proper set of itself.

If

A= {Dan, Volha, Serena}

A= {Dan, Volha, Serena}

Set A is equal set A, so it can not be a proper set of itself. They both have the same elements.