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![Math formula - Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_675136_2647e922_1773149672729_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=729_sc.jpg "Math formula - Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2\" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m Sets & Relations Complefe Formulas १. SETS BASIC DEFINITIONS 2. TYPES OF SETS Set: A well-defined collection of objects: Empty Null sef = only one element Singleton set Element: An object belonging to sef 2 Finite set belongs to A a € A Infinite set belong does nof To A U a#A Universal sef Equal sets Equivalenf sefs 3. SUBSETS ASB -> A is Q subsef of B 4. POWER SET Power set P(A) = set of all subsets of A A is a proper subset of B A subsef B ) elements, Then |P(A)| = 2\" Number of subsets of a set with n If A has 2n elements 6. PROPERTIES OF SET OPERATIONS 5. OPERATIONS ON SETS Commufqfive Iqws: AUB = BUA Union: AUB = {x : x E A or x & B} An B = BnA Intersection: AnB = {x:x eA and xeB} Associafive laws: (AUB)UC = AU(BUc) Difference: A - B = {x : x E A ond x E B} (AnB)nc=An(Bnc) Complement: A = U - A Disfribufive laws: Au(Bnc) = (AUB)n(Auc) An(BUC) = (AnB)U(AnC) Idenfify laws: AU0 = A AnU = A 7 DE MORGANS LAWS AUB) = AnB' 8. VENN DIAGRAM RESULTS (An B)' = A'UB' n(AUB) = n(A) + n(B) - n(AnB) n(A)+n(B)+n(C)-n(An B) n(AUBUC) n(Bnc) -n(CnA)+n(AnBnc) १०. TYPES OF RELATIONS ११. EQUIVALENCE RELATION 9. RELATIONS A relation R is an equivalence] A relation R from set A to set B Reflexive relqtion if it is: Symmetric subset of A x B is Reflexive Number of relafions from A fo B Symmetric Tronsitive Transitive 2nm (where n = elements in A, elements in B) m - ShareChat")
![biology - Reproduction Asexual Sexual (Need one parent) (Cont on next page) two (Need parents) Fragmentation Fission Regeneralion Budding Vegelative Spore Formalion Propagalion Eg. Rhizopus Breaks up into 2 or Broken parts of the inary Multiple organism grow into more small pieceS Artificial Natural ssion fission separate individuals e.g. Spirogyra. e.g. Planaria A Nucleus first divides into two Roots Leaves e.g. Bryophyllum 8.g Cytoplasm divides into two Dahlia TW0 daughter cells are formed e.g. Amoeba, Leishmania Stem Binger Nucleus divides repeatedly producing many nuclei of cytoplasm Each nucleus is surrounded by small] amount Gralting Culling Cysts breaks up and offsprings are liberated Scion Any part of a plant Portion grafted) e.g. Plasmodium is cut & buried | partly in moist soil Stock (Plant on which 8.9. /0$8. division cell grafted) repeated due to outgrowth A bud develops as an body Mango bud gets detached from parent e.g When matured, 2 individual is formed independent 3. A new Hydra yeast e.9. Layering produced Advontitious roots are Plant Is then detached ٥٠g Jasmine Reproduction Asexual Sexual (Need one parent) (Cont on next page) two (Need parents) Fragmentation Fission Regeneralion Budding Vegelative Spore Formalion Propagalion Eg. Rhizopus Breaks up into 2 or Broken parts of the inary Multiple organism grow into more small pieceS Artificial Natural ssion fission separate individuals e.g. Spirogyra. e.g. Planaria A Nucleus first divides into two Roots Leaves e.g. Bryophyllum 8.g Cytoplasm divides into two Dahlia TW0 daughter cells are formed e.g. Amoeba, Leishmania Stem Binger Nucleus divides repeatedly producing many nuclei of cytoplasm Each nucleus is surrounded by small] amount Gralting Culling Cysts breaks up and offsprings are liberated Scion Any part of a plant Portion grafted) e.g. Plasmodium is cut & buried | partly in moist soil Stock (Plant on which 8.9. /0$8. division cell grafted) repeated due to outgrowth A bud develops as an body Mango bud gets detached from parent e.g When matured, 2 individual is formed independent 3. A new Hydra yeast e.9. Layering produced Advontitious roots are Plant Is then detached ٥٠g Jasmine - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_46758_3174707f_1773023334719_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=719_sc.jpg "biology - Reproduction Asexual Sexual (Need one parent) (Cont on next page) two (Need parents) Fragmentation Fission Regeneralion Budding Vegelative Spore Formalion Propagalion Eg. Rhizopus Breaks up into 2 or Broken parts of the inary Multiple organism grow into more small pieceS Artificial Natural ssion fission separate individuals e.g. Spirogyra. e.g. Planaria A Nucleus first divides into two Roots Leaves e.g. Bryophyllum 8.g Cytoplasm divides into two Dahlia TW0 daughter cells are formed e.g. Amoeba, Leishmania Stem Binger Nucleus divides repeatedly producing many nuclei of cytoplasm Each nucleus is surrounded by small] amount Gralting Culling Cysts breaks up and offsprings are liberated Scion Any part of a plant Portion grafted) e.g. Plasmodium is cut & buried | partly in moist soil Stock (Plant on which 8.9. /0$8. division cell grafted) repeated due to outgrowth A bud develops as an body Mango bud gets detached from parent e.g When matured, 2 individual is formed independent 3. A new Hydra yeast e.9. Layering produced Advontitious roots are Plant Is then detached ٥٠g Jasmine Reproduction Asexual Sexual (Need one parent) (Cont on next page) two (Need parents) Fragmentation Fission Regeneralion Budding Vegelative Spore Formalion Propagalion Eg. Rhizopus Breaks up into 2 or Broken parts of the inary Multiple organism grow into more small pieceS Artificial Natural ssion fission separate individuals e.g. Spirogyra. e.g. Planaria A Nucleus first divides into two Roots Leaves e.g. Bryophyllum 8.g Cytoplasm divides into two Dahlia TW0 daughter cells are formed e.g. Amoeba, Leishmania Stem Binger Nucleus divides repeatedly producing many nuclei of cytoplasm Each nucleus is surrounded by small] amount Gralting Culling Cysts breaks up and offsprings are liberated Scion Any part of a plant Portion grafted) e.g. Plasmodium is cut & buried | partly in moist soil Stock (Plant on which 8.9. /0$8. division cell grafted) repeated due to outgrowth A bud develops as an body Mango bud gets detached from parent e.g When matured, 2 individual is formed independent 3. A new Hydra yeast e.9. Layering produced Advontitious roots are Plant Is then detached ٥٠g Jasmine - ShareChat")
![maths - G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_341722_306ef224_1772974340103_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=103_sc.jpg "maths - G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() - ShareChat")
![maths - G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_225870_2fd9d0ec_1772965212048_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=048_sc.jpg "maths - G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() G ٤ ٥ ٨ ٤ ٢ R 1 Jajaran cenjang Lingkacn Juring Tenbereng 2 (a+k) Apoeema K L= 4 . t Sudu+ yor berceccn berniiai /8oe L0 = 2/o Tropesium LA-Le স meno ೨' Karena LC Semberons 1.$1!0 ٢ ٢٥٥ ٥ ٥+٥ « ٤ lingkofon hodap diowerer K = 4+b +C +d 2 Beah ketupat] LF+Ld 4C+LE = | 00 k = TL x c L= T* T2 TL x 21 L.jucin9 x L ^03 2 ` d, ` d2 K = 4 x $ 3609 Layang -layang 0 Qanjang K busur %0 Panjarg Loc juring AOG k = 2 (AD+A৫) busur AD c luos lingkoon 2 % 02 Ka . lingkaran L= daiam Segitiga Lingkoron 21 ١ ٢ = [= Segitig 2 Kl Sudul' Jumtah !$($-)($-b)($ -c) f= Ietic SUdU+NYA $ Lingkaran luar Segitiga 180 0 bl a+btc K = a b c h- -|< $= Zx ^xt 2 4L L = I C Rumus Horon A *८ s (s-0)(S-b)ls-c) L٥ 4 ,$($-@)($-b)($-() - ShareChat")
