Materi Himpunan Jika [tex] A = \{a, b\}, B = \{c, d, e, f\}, \\ C = \{c, d, g\} [/tex] maka tunjukkan bahwa [tex] A \times (B \cap C) = (A \times B) \cap (A \ti

Bab Himpunan
Matematika SMP Kelas VII

A = { a, b }
B = { c, d, e, f }
C = { c, d, g }

A x (B ∩ C) = (A x B) ∩ (A x C)
{ a, b } x { c, d } = { ac, ad, ae, af, bc, bd, be, bf } ∩ { ac, ad, ag, bc, bd, bg }
{ ac, ad, bc, bd } = { ac, ad, bc, bd }

terbukti 

A = {a , b}
B = {c , d , e , f}
C = {c , d , g}

(B n C) = {c , d}
(A × B) = {ac , ad , ae , af , bc , bd , be , bf}
(A × C) = {ac , ad , ag , bc , bd , bg}


A × (B n C) = (A × B) n (A × C)
{a,b} × {c , d} = {ac,ad,ae,af,bc,bd,be,bf} n {ac,ad,ag,bc,bd,bg}
{ac,ad,bc,bd} = {ac,ad,bc,bd}

Jadi A × (B n C) = (A × B) n (A × C) => terbukti