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If U={2,3,5,7,9} is the universal set an...

If `U={2,3,5,7,9}` is the universal set and `A={3,7},B={2,5,7,9},` then prove that: `(AuuB)^'=A^(prime)nnB '` (ii) `(AnnB)^'=A^(prime)uuB '`

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To solve the problem, we will prove the two statements step by step. ### Given: - Universal Set \( U = \{2, 3, 5, 7, 9\} \) - Set \( A = \{3, 7\} \) - Set \( B = \{2, 5, 7, 9\} \) ### (i) Prove that \( (A \cup B)' = A' \cap B' \) ...
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"Let "A-={11,2,3,4,6},B{2,4,5,7,9}," then find "(i) AuuB(ii)AnnB

(a) If U= {1,2,3,……, 10} ,A = { 1,2,3,4,5}, B= {1,3,5,7,9} , C {2,4,8,10}, verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) (iii) A-B=AcapB^(c) (iv) Acap(BuuC)=(AcapB)uu(AcapC) . (b) If U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8} and B= {2,3,5,7}. Veify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

Knowledge Check

  • Let X = {1,2,3,4,5,6,7,8,9,10} be the universal set and A ={2,4,6,} , B = {1,3,7}, then A^(@) nn B^(@) is equal to .

    A
    `{2,4,5,6,7,8,9,10}`
    B
    `{1,3,5,7,8,9,10}`
    C
    X
    D
    `{5,8,9,10}`

  • If A=(-3,5) and B=[-7,9], then

    A
    A = B
    B
    `A sub B`
    C
    `B sub A`
    D
    None of these

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    Let U={1,2,3,4,5,6,7,8,9},A = {2,4,6,8} and B={2,3,5,7} . Verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

    If A={5,6,7,11},B={6,7,8,9} then show that A-B ,AnnB, B-A are disjoint sets

    If U" "={1," "2," "3," "4," "5," "6," "7," "8," "9" "} , A=" "{2," "4," "6," "8} andB" "=" "{" "2," "3," "5," "7} . Verify that (i) (AuuB)^(prime)=A^(prime)nnB^(prime) (ii) (AuuB)^(prime)=A^(prime)uuB^(prime)

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