InterviewSolution
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InterviewSolution
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Show that the following four conditions are equivalent : (i) `A sub B` (ii) `A - B = phi` (iii) `A cup B = B` (iv) `A cap B = A`. |
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Answer» (i) Let `A sub B` `rArr` All elements of A are in B (ii) `A - B = phi rArr` All elements of set A which are not in `B in phi` `rArr` There is no element in set A which is not in B `rArr` All elements of set A are in set B `rArr A sub B` `:. A- B = phi rArr A sub B` (iii) Let `A cup B = B` `because A sub A cup B` Therefore, `A sub B` [` because` Given `A cap B = B`] `:. A cup B = B rArr A sub B` (iv) Let `A cap B =A` `because A cap B sub B` `rArr A sub B` [ `because` Given `A cap B = A`] `:. A cap B = A rArr A sub B` Therefore, four conditions are equivalent. |
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