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![maths 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_356944_202b3fd9_1770956355480_sc.jpg?tenant=sc&referrer=pwa-sharechat-service&f=480_sc.jpg "maths 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")