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S Suraj Bhandari
If the number of elements in set A is equal to the number of elements in set B.

S Suraj Bhandari
The function sgn(x) is undefined at x=0. A function can be continuous or discontinuous at the points of domain not at points outside of the domain. Since {0} does not belong to the domain of sgn(x), the question of continuity or discontinuity is irrelevant.

S Suraj Bhandari
An identity relation on a set 'A' is the set of ordered pairs (a, a), where 'a' belongs to set 'A'. For example, suppose A={1,2,3}, then the set of ordered pairs {(1,1), (2,2), (3,3)} is the identity relation on set 'A'. Any relation 'R' on a set 'A' is said to be reflexive if (a, a) belongs to 'R', for every 'a' belongs to set 'A'. For example, suppose A={1, 2, 3}, then a relation...

S Suraj Bhandari
An empty set is a finite set having null element, that's why it is considered as subsets of all sets.

S Suraj Bhandari
When a=b then, ordered pair {a,b}={b,a} For a straight line y=x is an example.

S Suraj Bhandari
If U={1,2,3,4,5,6,7,8,9} is a universal set, A={1,2,3,4,}and B={3,4,5,6,7} are two sets then, (A âˆª B)={1,2,3,4,5,6,7} (A âˆª B)â€™={8,9} Aâ€™={5,6,7,8,9} B'={1,2,8,9} (Aâ€™ âˆ© Bâ€™)={8,9}

S Suraj Bhandari
If Universal set is not defined then the cardinal number is infinity otherwise it is equal to the total number of total elements.

S Suraj Bhandari
U-U'=U

S Suraj Bhandari
A-B=B-A={ }

S Suraj Bhandari
If both the sets are equal.

S Suraj Bhandari
No, it is just a symbol

S Suraj Bhandari
A. An empty set is a finite set having null element.

S Suraj Bhandari
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S Suraj Bhandari
YES, because in an empty set number of element is null.

S Suraj Bhandari
A Proper subset is defined as if the number of elements in the subset is not equal to the number of elements in parent set. And A Improper subset is defined as if the number of elements in the subset is equal to the number of elements in parent set.

S Suraj Bhandari
No, because in equivalence sets the number of elements is the same but in equal sets all elements are same.

S Suraj Bhandari
Understanding Sets, we can conceptualize and summarize the idea of similar objects and then on the basis of that only one can establish the attributes which in turn define them and make them unique. Further, it is the basic building block of Relations and Functions.
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