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If A={3,5,7,9,11},B={7,9,11,13},C={11,13...

If `A={3,5,7,9,11},B={7,9,11,13},C={11,13,15} and D={15,17},` find :
(i) `A cap B`
(ii) `B cap C`
(iii) `A cap C cap D`
(iv) `A cap C`
(v) `B cap D`
(vi) `A cap (B cup C)`
(vii) `A cap D`
(viii) `A cap (B cup D)`
(ix) `(A cap B) cap (B cap C)`
(x) `(A cup D) cap (B cup C)`.

Text Solution

Verified by Experts

(i) `A = {3,5,7,9,11} and B = {7,9,11,13}`
`A cap B = {7,9,11}`
(ii) `B={7,9,11,13} and C={11,13,15}BcapC={11,13}`
(iii) `A={3,5,7,9,11},C={11,13,15}and D={15,17}`
`A capC capD` = set of common elements of sets, A,C and D = { }
Therefore, `A cap C cap D = phi`
(iv) `A = {3,5,7,9,11} and C = {11,13,15} A cap C = {11}`
(v) `B = {7,9,11,13} and D = {15,17} B cap D = phi`
(vi) `A = {3,5,7,9,11}, B = {7,9,11,13} and C = {11,13,15}`
`B cup C = {7,9,11,13,15}`
`A cap (B cup C) = {7,9,11}`
(vii) `A = {3,5,7,9,11} and D = {15,17}`
`A cap D = phi`
(viii) `A = {3,5,7,9,11},B={7,9,11,13} and D={15,17}`
`B cup D = {7,9,11,13,15,17}`
`A cap (B cup D) = {7,9,11}`
(ix) `A = {3,5,7,9,11}, B = {7,9,11,13} and C={11,13,15}`
`AcapB={7,9,11}`
`B cupC={7,9,11,13,15}`
`:. (A cap B) cap (B cup C)=` set of common elements of the sets `(A cap B) and (B cup C) = {7,9,11}`
`:. (A cap B) cap (B cup C) = {7,9,11}`
(x) `A = {3,5,7,9,11},B={7,9,11,13}, C={11,13,15} and D= {15,17}`
`A cup D = {3,5,7,9,11,15,17}`
`B cup C = {7,9,11,13,15}`
`:. (A cap B) cap (B cup C)=` set of common elements of the sets `(A cap B) and (B cup C) = {7,9,11}`
`:. (A cap B) cap (B cup C) = {7,9,11}`
(x) `(A cup D) cap (B cup C) = ` set of common elements of sets `(A cup D) and (B cup C) = {7,9,11,15}`
Thereforem `(A cup D) cap (B cup X) ={7,9,11,15}`.
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