Let `A={x^(2) : x^(2) lt 50, x in N}` and `B={x : x" is a 2-digit number in which the sum of the digits is 7, "x in N}`.
(i) Draw Venn diagram to represent these sets. (ii) Find : (a) `A uu B` (b) `A nn B`
(c) `A-B` (d) `B-A`

Answer

(ii) (a) `{1, 4, 9, 16, 25, 34, 36, 43, 49, 52, 61, 70}`
(b) `{16, 25}`
(c) `{1, 4, 9, 36, 49}`
(d) `{34, 43, 52, 61, 70}`

Explanation

(i) `A={(1, 4, 9, 16, 25, 36, 49}`
`B={16, 25, 34, 43, 52, 61, 70}`
a and B have 16 and 25 as common elements. So, we draw two intersecting circles representing A and B respectively.

(a)`A uu B={1, 4, 9, 16, 25, 34, 36, 43, 49, 52, 61, 70}`
(b) `A nn B={16, 25}`
(c) `A-B={1, 4, 9, 36, 49}`
(d) `B-A={34, 43, 52, 61, 70}`