Question

A `A={3,6,9,12,15,18,21},B={4,6,12,16,20},C={2,4,6,8,10,12,14,16},D={15,10,15,20}`, Find :
(i) `A - B`
(ii) `A-C`
(iii) `A-D`
(iv) `B-A`
(v) `C-A`
(vi) `D-A`
(vii) `B-C`
(viii) `B-D`
(ix) `C-B`
(x) `D-B`
(xi) `C-D`
(xii) `D-C`.

Answer 1

(i) `A={3,6,9,12,15,18,21} andB={4,8,12,16,20}`
`A-B={x:x in A" but "x cancel(in)B}`
`={3,6,9,15,18,21}`
Therefore, `A-B={3,6,9,15,18,21}`
(ii) `A={3,6,9,12,15,18,21}`
and `C={2,4,6,8,10,12,14,16}`
`A-C={x:x in A " but " x cancel(in)C}`
Therefore, `A-C={3,9,15,18,21}`
(iii) `A={3,6,9,12,15,18,21} and {5,10,15,20}`
`A-D={x:x in A " but "x cancel(in)D}`
Therefore, `A-D={3,6,9,12,18,21}`
(iv) `A={3,6,9,12,15,18,12}`
and `B={4,8,12,16,20}`
`B-A={x:x in B" but "x cancel(in)A}`
`={4,8,16,20}`
Therefore, `B-A={4,8,16,20}`
(v) `A={3,6,9,12,15,18,21}`
and `D={5,10,15,20}`
`:. D-A={x:x in D " but "x cancel(in)A}`
`={5,10,20}`
Therefore, `D-A = {55,10,20}`
(vii) `B={4,8,12,16,20} and C={2,4,6,8,10,12,16}`
`B-C={x:x in B" but "x cancel(in)C}`
`= {2}`
Therefore, `B-C = {20}`
(viii) `B={4,8,12,16,20}and D={5,10,15,20}`
`B-D={x:x in B" but "x cancel(in)D}`
`={4,8,12,16}`
Therefore, `B-D = {4,8,12,16}`
(ix) `B={4,8,12,16,20}and C={2,4,6,8,10,12,14,16}`
`C-B={x:x in C" but "x cancel(in)B}`
`={2,6,10,14}`
Therefore, `C-B = {2,6,10,14}`
(x) `B={4,8,12,16,20}andD={5,10,15,20}`
`D-B={x:x in D " but "x cancel(in)B}`
`={5,10,15}`
Therefore, `D-B = {5,10,15}`
(xi) `C={2,4,6,8,10,12,14,16} and D={5,10,15,20}`
`C-D={x:x in C " but "x cancel(in)D}`
`={2,4,6,8,12,14,16}`
Therefore, `C-D = {2,4,6,8,12,14,16}`
(xii) `C={2,4,6,8,10,12,14,16} andD={5,10,15,20}`
`:. D-C={x:x in D " but "x cancel(in)C}`
`={5,15,20}`
Therefore, `D-C={5,15,20}`.