- #1

Keen94

- 41

- 1

## Homework Statement

Find the truth set of the given equivalence. Assume

*U*=ℝ

#56.

**(x**

^{2}=1)↔[(x=1)∨(x=-1)]Source:

__Principles of Mathematics__by Allendoefer and Oakley section 1.10

## Homework Equations

{x I p

_{x}↔q

_{x}}=(P∩Q)∪(P'∩Q')[/B]

## The Attempt at a Solution

P={x I p

_{x}}={x I x

^{2}=1}={x I x=1 or -1)

P'={x I x≠1 or -1}

Q={x I q

_{x}is true}={x I (x=1)∨(x=-1)}

q

_{x}=a

_{x}∨b

_{x}

{x I a

_{x}∨b

_{x}}=A∪B

Q=A∪B

Let a

_{x}be x=1 and b

_{x}be x=-1

A={x I a

_{x}} and B={x I b

_{x}}

A={1} and B={-1}

A∪B={-1,1}

Q={x I x=-1 or 1}

Q'={x I x≠-1 or 1}

(P∩Q)={x I x=1 or -1}∩{x I x=1 or -1}={x I x=1 or -1}

(P'∩Q')={x I x≠1 or -1}∩{x I x≠1 or -1}={x I x≠1 or -1}

(P∩Q)∪(P'∩Q')={x I x=1 or -1}∪{x I x≠1 or -1}=

*U*[/B]

Just wanted to know if someone could go over my work and verify it. Thank you for your time.