Show, for A = {X | X^2 + X - 6} and B = {-2, 3}, that...

[solomon_13000]

A = {X|X^2+X-6}
B = {-2,3}
A = B

The example above was given to me. How do I know A = B using the example above.

 

[pka]

Re: Sets

A = {X|X^2+X-6} & B = {-2,3} ->A = B
The example above was given to me. How do I know A = B using the example above.

What do you understand set equality to mean?
Can you give a definition? If you can, then the answer is obvious.

If you don’t know that definition, the you will have trouble with the answer.

 

[solomon_13000]

It means that elements for set A and B has to be the same.

 

[Gene]

Solve for X in X^2+X-6 (factor it)

 

[solomon_13000]

(x - 2)(x + 3) = 0

x = 2 x = -3

 

[Gene]

Hmmmm!
(x-2)(x+3) = 0
so what are the possible values of x that make it true?
Hint: either (x-2) = 0 or (x+3) = 0

 

[pka]

It means that elements for set A and B has to be the same.

Well actually the formal definition is:
\(\displaystyle \L A = B\quad \Leftrightarrow \quad A \subseteq B\quad \& \quad B \subseteq A\)

 

[solomon_13000]

2 - 2 = 0

-3 + 3 = 0

so that means that A = B

 

[stapel]

A = {X|X^2+X-6}

As given, the set A is just "all x", since "x² + x - 6" does not restrict the value of x at all.

Did you perhaps mean A to be {x | x² + x - 6 = 0}...?

Thank you.

Eliz.