If set A is a proper subset of setB and set B belongs to setC then will set a belong to set C?

it is given in a book that a will not belong to c .but how?

alsi for a set to belong to some other set is it essential that all elements of one set should be present in the other.

If set A is a proper subset of setB and set B belongs to setC then will set a belong to set C?c++ compiler

Not necessarily. A note to the above answerer: "belongs to" is not ambiguous in any way. If x belongs to X, then x is an element of X. It's fairly standard terminology.

So here's the problem:

C is a set of sets. The set B is in C.

The set A might be in C. Is it?

A=B is not an option, however. Because A is a proper subset of B. There is no rule that says if C contains B, then C must contain all of its proper subsets.

Thus the answer is no (not necessarily).

Example: C is the set of {my cat, my marbles, my TV}

B = my marbles

A = my green marbles

C does not contain "my green marbles" - even though it contains "my marbles" because we're not talking about which marbles it contains, we're talking about two distinct sets of marbles.

If set A is a proper subset of setB and set B belongs to setC then will set a belong to set C?c++ cli

I think what the book is trying to point out is the loose terminology in the question.

If the question said:

" If A is a proper subset of B and set B IS A PROPER SUBSET OF C then will A BE A PROPER SUBSET of C?"

This is a true statement.

Being a "subset of" another set is different from "belonging to" a set.

Consider the following example:

A = {1, 2, 3}

B = {1, 2, 3, 4, 5}

and C = { {1, 2, 3, 4, 5}, {1, 2} }

Certainly A is a proper subset of B, each containing numbers.

C, on the other hand, is a set of sets. It contains B, but the set A is not contained in set C.

Does this help?

If set A is a proper subset of setB and set B belongs to setC then will set a belong to set C?

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