Question

give all formula for sets​

Answer 1

Question

give all formula for sets

Answers

Formulas of Sets

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)

Request

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Answer 2

Answer:

A cartesian product A × B of two sets A and B is given by:

A × B = { \((a,b):a\epsilon A, b\epsilon B\) }

If (a , b) = (x , y); then a = x and b = y

If n(A) = x and n(B) = y, then n(A × B) = xy

A × \(\phi\) = \(\phi\)

The cartesian product: A × B ≠ B × A

A function f from the set A to the set B considers a specific relation type where every element x in the set A has one and only one image in the set B.

A function can be denoted as f: A → B, where f(x) = y

Algebra of functions: If the function f: X → R and g: X → R; we have:

(i) \((f + g) (x) = f (x) + g(x),

(i) \((f + g) (x) = f (x) + g(x), x\epsilon X\)

(ii) \((f – g) (x) = f (x) – g(x), x\epsilon X\)

(iii) \((f.g)(x) = f (x) .g (x), x\epsilon X\)

(iv) \((kf) (x) = k ( f (x) ), x\epsilon X\), where k is a real number

(v)\( \frac{f}{g}(x) = \frac{f(x)}{g(x)}, x\epsilon X, g(x)\neq 0\)