(i) False
No, it is not necessary for the any two set A and B to be either A B or B A.
(ii) False
Here, A = {1,2,3} It is the finite subset of infinite set N of natural numbers.
(iii) True
The logically smaller part of something finite can never be infinite.
Therefore, every subset of a finite set is finite.
(iv) False
Since, null set or empty set does not have a proper subset.
(v) False
We do not repeat elements in a set, therefore the given set becomes {a, b} which is a finite set.
(vi) True
The equivalent sets have same number of elements.
(vii) False
In A = {1}
Hence, the subsets can be ϕ and {1} which are finite.