proper subset sentence in Hindi

Examples

1. If a set and has the same cardinality as a proper subset of itself, then it's an infinite set.
2. A system of equations if " independent " if it is not equivalent to a proper subset of itself.
3. A frame is an " exact frame " if no proper subset of the frame spans the inner product space.
4. I therefore consider " toroids " to be a proper subset of all " surfaces / solids of revolution ".
5. If I and J are stable models of the same logic program then I is not a proper subset of J.
6. Any proper subset of a finite set " S " is finite and has fewer elements than " S " itself.
7. In 1881 he set out the set that can be put into a one-to-one correspondence with one of its proper subsets.
8. A generating set of a module is said to be "'minimal "'if no proper subset of the set generates the module.
9. The first two complement laws above show that if is a non-empty, proper subset of, then } } is a partition of.
10. Actually, proper subsets of \ mathfrak X may host sentineling tasks that prove harder than those emerging with \ mathfrak X itself.