If A and B are subsets of the universal set U, then slow that
(i) `A sub A uu B` , (ii) `A sub B hArr A uu B = B`
(iii) `(A nn B) sub A`

Explanation

(i) Let `x in A`
` rArr x in A ` or `x in B rArr x in A uu B`
Hence, `sub A uu B`
(ii) If `A sub B`
Let `x in A uu B`
`rArr x in A ` or `x in B rArr x in B , [:' A sub B]`
`rArr A uu B sub B "……"(i)`
But `B sub A uu B "......"(ii)`
From Eqs. (i) and (ii).
`A uu B = B`
If ` A uu B = B`
Let ` y in A`
`rArr y in A uu B rArr y in B , [:' A uu B = B]`
`rArr A sub B`
Hence, `A sub B hArr A uu B = B`
(iii) Let `x in A nn B`
`rArr x in A` and `x in B rArr x in A`
Hence, `A nn B sub A`