Page 28 - Kelompok 8_Proyek
P. 28
i. Bersifat tertutup terhadap penjumlahan
∀ , ∈ berlaku
2
2
+ = + + + ⋯ + + ⋯ + + + + ⋯ + + ⋯
0
2
1
2
0
1
= + ) + + + ⋯ + ( + ) + ⋯
0
0
1
1
(karena bersifat tertutup terhadap penjumlahan di R)
2
= + + ⋯ + + ⋯ ∈ [ ]
0
1
dengan = σ =0 ( + ) ∈
ii. Bersifat assosiatif terhadap penjumlahan
∀ , , ℎ ∈ [ ]
+ + ℎ = + + ⋯ + + ⋯ + + + ⋯ + + ⋯
1
0
1
0
2
+ + + + ⋯ + + ⋯
1
0
2
2
= + ) + + + ⋯ + ( + ) + ⋯ +] + + + + ⋯ + + ⋯
0
1
1
2
0
1
0
= + ) + ] + + 1 + + ⋯ + [ + + ] + ⋯
1
0
0
1
0
= + + 0 + [ + ( + )] + ⋯ + [ + ( + )] + ⋯
1
1
1
0
0
(karena bersifat assosiatif terhadap penjumlahan di R)
= + + ⋯ + + ⋯ + + 0 + ( + + ⋯ + ( + )] + ⋯ ]
0
1
1
1
0
2
= + + ⋯ + + ⋯ + [ + + ⋯ + + ⋯ + + + + ⋯ + + ⋯ ]
2
1
0
1
0
1
0
= + [ + ℎ ]
∴Terbukti [ +] + ℎ ] = ( ) + [ + ℎ ]
