Question

If U= {3, 5, 7, 9, 11, 13, 15} and A = {3, 5, 7} then its complement is​

Answer 1

Answer:

A={3,5,7,9,11},B={7,9,11,13},C={11,13,15} and D={15,17}

(i) A∩B={7,9,11}

(ii) B∩C={11,13}

(iii) A∩C∩D=(A∩C)∩D={11}∩{15,17}=ϕ

(iv) A∩C={11}

(v) B∩D=ϕ

(vi) A∩(B∪C)=(A∩B)∪(A∩C)

={7,9,11}∪{11}={7,9,11}

(vii) A∩D=ϕ

(viii) A∩(B∪D)=(A∩B)∪(A∩D)

={7,9,11}∪ϕ={7,9,11}

(ix) (A∩B)∩(B∪C)={7,9,11}∩{7,9,11,13,15}={7,9,11}

(x) (A∪D)∩(B∪C)={3,5,7,9,11,15,17}∩{7,9,11,13,15}

={7,9,11,15}

please mark me as brilliant

Answer 2

Answer:

${\huge{\pink{↬}}} \:  \: {\huge{\underline{\boxed{\bf{\pink{Answer}}}}}}$

A = = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

(i) AnB = {7,9,11}

(ii) BnC = {11, 13}

(iii) AncnD= (ANC) nD={11}

{15, 17} = 0

(iv) AnC = {11}

(v) BnD=

(vi) An (BUC) = (ANB)U(ANC) = {7,9,11} U{11} = {7,9,11}

(vii) AnD = o

(viii) An (BUD) = (ANB) U (AND) = {7,9,11} U = {7,9,11}

(ix) (An B) n (BUC) = {7,9,11} {7, 9, 11, 13, 15} = {7,9,11}

(x) (AUD) n (BUC) = {3,5,7,9, 11, 15, 17}

{7, 9, 11, 13, 15}

= {7,9,11,15}