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What is a subset in maths?
A set "A" is said to be a subset of of set "B", if every element in set "A" is also an element of set "B". If "A" is a subset of "B" and the sets are not equal, "A" is said to be a proper subset of "B". For example: the set of natural numbers is a subset of itself. The set of square numbers is a subset (and also a proper subset) of the set of natural numbers.
Difference between subset and proper subset?
A subset of a set S can be S itself. A proper subset cannot.
Can an empty set be a subset and a proper subset?
Yes.
What is a proper subsets?
Proper subset definitionA proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in Abut A contains at least one element that is not in B.For example, if A={1,3,5} then B={1,5} is a proper subset of A. The set C={1,3,5} is a subset of A, but it is not a proper subset of A since C=A. The set D={1,4} is not even a subset of A, since 4 is not an element of A.
Is an empty set a subset of every set?
Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.
