HW 4 Solution

7.2 Civ) : 7- MEZT , th C- Zt , men .

pf : True - Let M=l . Foh tht# i n > I.

•

7.3 : CV) : Fritz , 7-MEN , MEN .

pf : True .

For KNEZ , h- IEZ sat . n- Ish.

So let M=h- I.

Dk

di) INEZ , tmEZ , MEN .

Pt : False . Let's prove the negation : Antz , 7-MEK , man .

For they let m- htt . Then M >n .

DA

Problem I :

II.Civ) VXEIR ,7- YER , Xy > 0.

Pt : pintle -

she negation . HEIR , VTGIR , +9=0 .

Let x=o , then Hy EIR , x.y -OEO .

By

(V) : 7-XER , Hy EIR , Xy 70 .

Pf : False . To show the negation : ht XEIR , 7-YER , Xy so .

For HER , IET y =-X ,

X - y = X. C-X) = - X'EO

.

Dhs

(Vi) : HEIR, 7-YER , xyx0 -

Pf : True .For VXEIR , let y=x .

X - y = X - X = XZ 70 .

A

Lvii) 7-XEIR , byEIR i xy 70 .

Pf : True . Let X- o , then HyEIR , X - y = 070

Dk

Lviii) KXEIR , IYER , Cxty >o or xty=o ) .

Pt : True . For UXEIR , let y - -X .

Then Xty = X-x = o .

•

(IX) VVER ,7-JER , City > o and xty=o) .

Pf : False . Prove the negation : HEIR , Hyuk , Atyeo or xty#o) .

For X=o , Hy ER , if y so . ,then Xty = y ⇐ o .

if y >o , then Xty = y > 0 Go to).

Ba