1. ## Set Theory Please Check my Work!

Hello! These are two questions I am unsure on for my homework.

Which of these symbols is used to indicate a comparison between two sets?

Union
Intersection
Subset
Cartesian Product
Null Space

Work: I think it's intersection. But I don't know..

To prove that A ∪ A = A , each of the following steps can be performed ( where U indicates the universal set ).
A = ( A ∪ A ) ∩ U by the identity law of intersection
A = ( A ∪ A ) ∩ ( A ∪ A c )by the complement law for union
A = A ∪ ( A ∩ A c ) by the distributive law of union over intersection

A = A ∪ ∅ by the complement law for intersection
A =A by the identity law for union

True or False.

Work: False, because the 2 to 3rd set doesnt make sense.

TIA!

2. Originally Posted by aeubz
Hello! These are two questions I am unsure on for my homework.

Which of these symbols is used to indicate a comparison between two sets?

Union

Intersection

Subset

Cartesian Product

Null Space

Work: I think it's intersection. But I don't know..

To prove that A ∪ A = A , each of the following steps can be performed ( where U indicates the universal set ).

A = ( A ∪ A ) ∩ U by the identity law of intersection

A = ( A ∪ A ) ∩ ( A ∪ A c )by the complement law for union

A = A ∪ ( A ∩ A c ) by the distributive law of union over intersection

A = A ∪ ∅ by the complement law for intersection

A =A by the identity law for union

True or False.

Work: False, because the 2 to 3rd set doesnt make sense.

TIA!