A = {1, 2, {3, 4}, 5}
(i) The statement {3, 4} \(⊂ A\) is incorrect because 3\(∈\) {3, 4}; however, \(3 ∉ A.\)
(ii) The statement {3, 4}\(∈ A\) is correct because {3, 4} is an element of A.
(iii) The statement {{3, 4}} \(⊂ A\) is correct because {3, 4} \(∈\) {{3, 4}} and {3, 4}\(∈ A.\)
(iv) The statement 1 \(∈ A\) is correct because 1 is an element of A.
(v) The statement 1\(⊂ A\) is incorrect because an element of a set can never be a subset of itself.
(vi) The statement {1, 2, 5} \(⊂ A\) is correct because each element of {1, 2, 5} is also an element of A.
(vii) The statement {1, 2, 5} \(∈ A\) is incorrect because {1, 2, 5} is not an element of A.
(viii) The statement {1, 2, 3} \(⊂ A\) is incorrect because \(3 ∈\) {1, 2, 3}; however, 3 A.
(ix) The statement \(\phi∈ A\) is incorrect because \(\phi\) is not an element of A.
(x) The statement \(\phi ⊂ A\) is correct because \(\phi\) is a subset of every set.
(xi) The statement {\(\phi\)} \(⊂ A\) is incorrect because \(\phi ∈\) {\(\phi\)}; however, \(\phi∈ A.\)
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: