Quiz 3
Quiz 3
Friday, March 30, 2001
NAME:
Student Number:_{------}
No._{----} Marks _{----}
(25 Marks) Let A and B be two sets.
Prove that
Proof.
(i) We prove that [`(AÇB)] Ì [`A]È[`B].
In fact, let x Î [`(AÇB)]. Then x Ï AÇB. This
implies x Ï A or x Ï B. Hence, x Î [`A] or x Î [`B], that is, x Î [`A]È[`B].
(ii) We prove that [`A]È[`B] Ì [`(AÇB)].
Since AÇB Ì A and AÇB Ì B, we have
This implies [`A]È[`B]È[`(AÇB)].
By (i) and (ii), we obtain [`(AÇB)] = [`A]È[`B].
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On 3 Apr 2001, 10:18.