sets chapter all formula
Answers
Step-by-step explanation:
SYMBOL - SET
N The set of all the natural numbers
Z The set of all the integers
Q The set of all the rational numbers
R The set of all the real numbers
Z+ The set of all the positive numbers
Q+ The set of all the positive rational numbers
R+ The set of all the positive real numbers
1) The union of two sets A and B are said to be contained elements that are either in set A and set B. 2)The union of A and B is denoted as: \(A\cup B\).
3) The intersection of two sets A and B are said to be contained elements that are common in both the sets. 4) The intersection of A and B is denoted as: \(A\cap B\).
5) The complement of a set A is the set of all elements given in the universal set U that are not contained in A. 6) The complement of A is denoted as \({A}’\).
7) For any two sets A and B, the following holds true:
(i) \({(A\cup B)}’={A}’\cap{B}’\)r
(ii) \({(A\cap B)}’={A}’\cup{B}’\)
8) If the finite sets A and B are given such that \({(A\cap B)}=\phi\), then: \(n{(A\cup B)}=n(A)+n(B)\)
If \({(A\cup B)}=\phi\), then: \(n{(A\cup B)}=n(A)+n(B)-n(A\cap B)\)
These are the basic set of formulas from the set theory.
If there are two sets P and Q,
n(P U Q) represents the number of elements present in one of the sets P or Q.
n(P ⋂ Q) represents the number of elements present in both the sets P & Q.
n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q)
For three sets P, Q, and R,
n(PUQUR)=n(P)+n(Q)+n(R)–n(P⋂Q)–n(Q⋂R)–n(R⋂P)+n(P⋂Q⋂R)