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R -S = { t|t∈R?t?S } μ μ (? ? ) ABC a1 b1 c1 a1 b2 c2 a2 b2 c1 R ABC a1 b1 c1 R-S ABC a1 b2 c2 a1 b3 c2 a2 b2 c1 S 3. ? ? Intersection  z R?S – μM]¥ " n – M?¥ ?? |1]B?× z R?S – ˉ1 n "1"?; ?? R? ?? S¥íFF? R?S = { t|t ∈ R?t ∈S } R?S = R –(R-S ? ? (? ? ) ABC a1 b1 c1 a1 b2 c2 a2 b2 c1 R ABC a1 b2 c2 a2 b2 c1 R ?S ABC a1 b2 c2 a1 b3 c2 a2 b2 c1 S 4. <l2 5: <l2 5:   Extended Cartesian Product  z R – n "1" k 1 ?íF z S – m "1" k 2 ?íF z R?S –  n+m ¥íF¥"? z íF¥ - n  ^1" R¥B?íF z a m  ^1" S¥B?íF – ? k 1 ?k 2 ?íF z R?S = {t r t s |t r ∈R?t s ∈S } <l2 5: <l2 5: (? ? ) ABC a1 b1 c1 a1 b1 c1 a1 b1 c1 a1 b2 c2 a2 b2 c1 a2 b2 c1 a2 b2 c1 a1 b2 c2 a1 b2 c2 ABC a1 b2 c2 a1 b2 c2 a1 b2 c2 a1 b3 c2 a2 b2 c1 a1 b3 c2 a2 b2 c1 a1 b3 c2 a2 b2 c1 ABC a1 b1 c1 a1 b2 c2 a2 b2 c1 R R ?S ABC a1 b2 c2 a1 b3 c2 a2 b2 c1 S 2.2 1"} ? 1"} ? z à ? z .d¥"? ? z  ê¥1" ? 2.2.2  ê¥1" ?  ê¥1" ? z ê4 z g? z ?¤ z " 1. ê4 ê4 Selection  z 1) ê4??1K? Restriction z 2) ê4 ??¥cl – 1" R?ê4 ?@ó?Hq¥ííF 6 F (R) = {t|t∈R?F(t)= '?'} – Fê4Hq ^B? ? Vr T'? T1 X 1 , Y 1 [9 X 2 , Y 2 ]… z ,1? ?? #?!?" <> z X 1  Y 1 ? ?? aè ae?f ? ?? 9 V [ ¨ ? ¥?| ?}9 z 9 ?  ?? ?? z [ ]V U ?ê[ z …V U  ?ì T V[×ˉ/ ? ê4 ê4   ? ? z 3) ê4 ? ^V?¥?é?¥ ? z 4)  è !μB?D 3 - [? ? o ?D 31 " Studenta [?1" Course?ê?1" SCb 6 ê4 ê4   ? ? Student D| Sno ? Sname ?Y Ssex M - Sage ?" Sdept 95001 ù§ 3 20 CS 95002 >? o 19 IS 95003 | ù o 18 MA 95004 f ? 3 19 IS è 1 è 2 è 4 è 3 ê4 ê4   ? ? Course (b) [?| [? 5? [ Ds Cno Cname Cpno Ccredit 1 ? o 5 4 2 ?D 2 3 ?"d 1 4 4 ?T"d 6 3 5 ? 2 7 4 6 ? ) ? 2 7 PASCAL?y 6 4 è 9 ê4 ê4   ? ? SC D| [?| ? Sno Cno Grade 95001 1 92 95001 2 85 95001 3 88 95002 2 90 95002 3 80 (c) è 7 è 9 ê4 ? ê4 ? [ è 1] °??" IS" ?8D 3 6 Sdept = 'IS' (Student) 6 5 ='IS' (Student) 2T Sno Sname Ssex Sage Sdept 95002 >? o 19 IS 95004 f ? 3 19 IS ê4 ? ê4 ? [ è 2] °? M -l? 20 ?¥D 3 6 Sage < 20 (Student) 6 4 < 20 (Student) 2T Sno Sname Ssex Sage Sdept 95002 >? o 19 IS 95003 | ù o 18 MA 95004 f ? 3 19 IS 2. g? g? Projection  z 1g? ??¥cl – V R?ê4 ?? ?? F??¥1" 4 A (R) = { t[A] | t ∈R } A R?31 =¥ ??  2. g? g? Projection  z 2g??T?1 ^V ¥?é? ? – ?g?-a?? |h e1"?¥ t  7 O? V ? |h tíF E ?×ˉ? 4 g? g?   ? ? z 3)  è [ è 3] °?D 3¥? ? ?" ' p Student1" D 3? ? ?" ? ? ? ¥g? 4 Sname Sdept (Student) 4 2 5 (Student) 2T g? g?   ? ? Sname Sdept ù§ CS >? IS | ù MA f ? IS g? g?   ? ? [ è 4] °?D 31" Student??μ 't" 4 Sdept (Student) 2T Sdept CS IS MA 3. ?¤ ?¤ Join  z 1 ?¤9?1, ?¤ z 2 ?¤ ?¥cl – V ?1"¥2 5:?ê | ??W ?@B?Hq ¥íF R S = { | t r ∈ R?t s ∈S?t r [A], t s [B] } z A?B sY1 R?S  ?M? O V1¥ ??F z ,1? ?? – ?¤ ?V R?S¥<l2 5: R?S?ê | R1 " A ??F ¥′D S1" B ??F ′ ?@1?1"¥íFb A, B t r t s ?¤ ?¤ (? ? ) z 3  ?è¨ ?¤ ? – ?′ ?¤ equijoin z I 1 ^?′ ?¤ –,1 “" ”¥ ?¤ ??1?′ ?¤ z ?′ ?¤¥cl –V1" RD S¥<l2 5:?ê | AaB ?? ′M?¥ *tíF'?′ ?¤1 R S = { | t r ∈R?t s ∈S?t r [A] = t s [B] } A=B t r t s ?¤ ?¤ (? ? ) – 1 ? ?¤ Natural join z I 1 ^1 ? ?¤ – 1 ? ?¤ ^B?+ y¥?′ ?¤ ? ?1"?é?1?¥s A? ^M] ¥ ??F ? 2T?ü×ˉ¥ ??  ?? z 1 ? ?¤¥cl R?S μM]¥ ??F B RS= { | t r ∈R?t s ∈S?t r [B] = t s [B] } t r t s ?¤ ?¤ (? ? ) z 4B?¥ ?¤?T ^V?¥?é?  ?b 1 ? ?¤?31 |h×ˉ  ?[ ^ ] HV?? ¥?é? ?b A, B R S ?¤ ?¤ (? ? ) z 5  è [ è 5] B E b 1 3 b 2 7 b 3 10 b 3 2 b 5 2 A B C a 1 b 1 5 a 1 b 2 6 a 2 b 3 8 a 2 b 4 12 R S ?¤ ?¤ (? ? ) R S A R.B C S.B E a 1 b 1 5 b 2 7 a 1 b 1 5 b 3 10 a 1 b 2 6 b 2 7 a 1 b 2 6 b 3 10 a 2 b 3 8 b 3 10 C! E ?¤ ?¤ (? ? ) ?′ ?¤ RS R.B=S.B A R.B C S.B E a 1 b 1 5 b 1 3 a 1 b 2 6 b 2 7 a 2 b 3 8 b 3 10 a 2 b 3 8 b 3 2 ?¤ ?¤ (? ? ) 1 ? ?¤ RS A B C E a 1 b 1 5 3 a 1 b 2 6 7 a 2 b 3 8 10 a 2 b 3 8 2 4. " " Division  ó?1" 3 9 : ? 4 : ;  ? 9 : ;1 ?? Fb 3?¥ :D 4?¥ : V[μ?]¥ ?? ? A?1M] ¥×" b3D 4¥" ?¤?B??¥1" 1 9  R?S = P(x)  |t∈P(X), μ t ∈4 X (R), 7 O t ?4 Y (S) ? R " " (? ? ) z 2"?T ^] HV?? ?é? ? z 3  è [ è 6] ? R S " " (? ? ) A B C a 1 b 1 c 2 a 2 b 3 c 7 a 3 b 4 c 6 a 1 b 2 c 3 a 4 b 6 c 6 a 2 b 2 c 3 a 1 b 2 c 1 B C D b 1 c 2 d 1 b 2 c 1 d 1 b 2 c 3 d 2 R?S A a 1 R S 2.2.3 ¨1"} ?V U1"?T ¨1"} ?V U1"?T [ è 1] °?D [?|1 1137¥D 3¥ D|?? 4 Sno,Grade (6 Cno=‘1137 ( SC)) 2.2.3 ¨1"} ?V U1"?T ¨1"} ?V U1"?T [ è 2] °?D [?|1 1137¥D 3¥ D|?? 4 Sno,Sname ( S (6 Cno=‘1137 ( SC)) ) [ è 5] °?à ê? [?|1 1024?1136 ¥D 3¥D| 4 1 (6 1=4^2=‘1024’^5=’1136’ ( SC ? SC) ) l2 l2 z1"} ? ? – 1"} ? ? iaμa?a2 5:ag?aê4a ?¤a" – ' ? iaμa2 5:ag?aê4 – ?a ?¤a" V[¨ 5?' ? ?Vr / [ bbb ¨B?8bbb