Question

Proper subset of natural numbers

Answer 1

Answer:

Proper Subset: If A and B are two sets, then A is called the proper subset of B if A ⊆ B but B ⊇ A i.e., A ≠ B.

...

Subset

Let A = {2, 4, 6} B = {6, 4, 8, 2} ...

The set N of natural numbers is a subset of the set Z of integers and we write N ⊂ Z.

Let A = {2, 4, 6} ...

Let A = {1, 2, 3, 4}

Answer 2

Answer:

Proper Subset:

If A and B are two sets, then A is called the proper subset of B if A ⊆ B but B ⊇ A i.e., A ≠ B. The symbol ‘⊂’ is used to denote proper subset. Symbolically, we write A ⊂ B.

For example;

1. A = {1, 2, 3, 4}

Here n(A) = 4

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

Here n(B) = 5

We observe that, all the elements of A are present in B but the element ‘5’ of B is not present in A.

So, we say that A is a proper subset of B.

Symbolically, we write it as A ⊂ B

Notes:

No set is a proper subset of itself.

Null set or ∅ is a proper subset of every set.

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