Perbaikan final PA 2012

Terlampir perbaikan final PA, sebelumnya kan semifinal PA...hehehe


http://www.ziddu.com/download/21304772/PerbaikanPAfinal2013.pdf.html

UTS STRUKTUR ALJABAR 1 dan VARKOM UNIBBA

Berikut Tata cara mengerjakan UTS varkom dan StrukAl take home test
 
http://www.ziddu.com/download/21191530/UTSVARKOMdanSTRUKTURALJABARIUNIBBA.pdf.html

SOAL PA NOMOR 5

5a. Show that if f maps X into Y and A is a subset of X, B is a subset of  Y then

f(f^(-1)(B)) is a subset of B

NB : f^(-1) is the inverse image ( peta invers).

5b. Show that if  f  maps X onto Y and B is a subset of Y, then 

f(f^(-1)(B)) = B

NB :  f  maps X onto Y = f onto/surjective ( pada)

SOAL PA NOMOR 4

4a. Prove that every integer is either even or odd, but never both.

4b. Prove that if b > 0 then b|a if and only if a mod b = 0.

SOAL PA NOMOR 3

Let n be a positive integer. Prove the square root of n is either n integer or it is irrational.

SOAL PA NOMOR 2

Prove if a be an arbitrary real number then for arbitrary integers m and n we have :

(i). a^m . a^n = a^(m+n)

(ii) (a^m)^n = a^(mn)

SOAL NOMOR 1 PA

Prove

(cos x +i sin x)^n = cos (nx) + i sin (nx)

valid for any real number x and for any integer n.

NB : (cos x +i sin x)^n = (cos x +i sin x) to the power of  n