(i) It can be seen that A \(⊂\) {0, 1, 2, 3, 4, 5, 6}
B \(⊂\) {0, 1, 2, 3, 4, 5, 6}
However, C \(\not\subset\) {0, 1, 2, 3, 4, 5, 6}
Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C.
(ii) \(A \not\subset \phi, B \not\subset \phi, C \not\subset \phi\)
Therefore, \(\phi\) cannot be the universal set for the sets A, B, and C.
(iii) A \(\subset\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B \(\subset\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C \(⊂\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.
(iv) A \(⊂\) {1, 2, 3, 4, 5, 6, 7, 8}
B \(\subset\) {1, 2, 3, 4, 5, 6, 7, 8}
However, C \(\not\subset\) {1, 2, 3, 4, 5, 6, 7, 8}
Therefore, the set {1, 2, 3, 4, 5, 6, 7, 8} cannot be the universal set for the sets A, B, and C.
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
Sets are of various types depending on their features. They are as follows: