Question

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2. Prove that the following statements are true for sets A, B, C: (a) Commutativity (I): An B = BNA. (b) Commutativity (II): AU B = BU A. (c) Distributivity (I): AN(BUC) = (AN B)U(ANC). (d) Distributivity (II): AU (BAC) = (AUB) N (AUC). (e) Idempotence (I): An A = A. (f) Idempotence (II): AU A = A.

Answer 1

2 (4). Cоm mаtаtіvfy t) ADB = BOA det XGAMB -xeA Cind acB е зее аnd хел е ас-ВРА - Аов — BOA (b) д) AU19 - BOA det XE AVB — хєА от хев kỳ 3 ( 8 03 3 XEBUA > AUBBUA (6) Distributivity D A CAUC = (ANB) OCADO Leta EADCBU) — хєA and ae 80 с EX EA and acB or xe c Xen and WEB OY XCA OTHEC е е АПВ ст хєАЛС - хє САПВ) O CA0 с) ADIBUC) = CAN B) UCANC)

roll Distophet inity I) AUCANO) = (AUB) OCAUC) 1е е лоСВЛc) Y XGA or XEBOC ☆ XCA or X€ß and aec НасA ox xcB and хед от хес XE AUB and we AUC XE CAUB) DCADO) 5 AUCBD 0 = (AUB) OCAUC) (e) Idempotence (D) ADAFA 1-el xc AOA — яе 4 4 хед excA - ADA = A (f) Idempotence (IT) MUA: A let xEAUA G ac A oraf A + AUNEA XEA Hence proved