Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Complement of Set A

Let A bar = complement of set A = A_c.

If A is a set, the complement of A, denoted A bar or A_c, is the set consisting of all the elements in the universe set that are not in set A.

Let U = universe set

Let A = set A

Let A bar or A_c = complement of set A

U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }

A = { 1, 3, 5, 7, 9 }

I can then say that A bar or A_c = { 2, 4, 6, 8 }.

Let U = union of two sets

Let n = intersection of two sets

It follows from the definition of complement that A U A bar and A n A bar = empty set. Can you tell me why that is the case?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Complement of Set A

The latex for union is \cup and intersection \cap but they don't seem to work for me so I'll use the words instead.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Complement of Set A

The latex for union is \cup and intersection \cap but they don't seem to work for me so I'll use the words instead.

Bob

What do you mean by cup?

What do you mean by cap?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Complement of Set A

cup = union symbol
cap = intersection symbol.

When I want a post to show 'nicely' formatted maths I use Latex code.  \cup should produce a proper union symbol (not just a capital U) but the forum code checker gave a syntax error.  So I just removed the \ .

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Complement of Set A

cup = union symbol
cap = intersection symbol.

When I want a post to show 'nicely' formatted maths I use Latex code.  \cup should produce a proper union symbol (not just a capital U) but the forum code checker gave a syntax error.  So I just removed the \ .

Bob

I don't understand LaTeX for the life of me.