How to read / present math in English?

How to read / present math, equation, formula in English? 

1. Logic

∃ there exist
∀ for all
pp implies q / if p, then q
pp if and only if q /p is equivalent to q / p and q are equivalent

2.Sets

xx belongs to A / x is an element (or a member) of A
xx does not belong to A / x is not an element (or a member) of A
AA is contained in B / A is a subset of B
AA contains B / B is a subset of A
AA cap B / A meet B / A intersection B
AA cup B / A join B / A union B
A\B A minus B / the difference between A and B
A×B A cross B / the Cartesian product of A and B

3. Real numbers

x+1 x plus one
x-1 x minus one
x±1 x plus or minus one
xy xy / x multiplied by y
(x-y)(x+y) x minus y, x plus y
the equals sign
x=5 x equals 5 / x is equal to 5
x≠5 x (is) not equal to 5
xx is equivalent to (or identical with) y
x>y x is greater than y
x≥y x is greater than or equal to y
x<y x is less than y
x≤y x is less than or equal to y
0<x<1 zero is less than x is less than 1
0≤x≤1 zero is less than or equal to x is less than or equal to 1
|x| mod x / modulus x
x2  x squared / x (raised) to the power 2
x3  x cubed
x4  x to the fourth / x to the power 4
xn  x to the nth / x to the power n
x (−n) x to the (power) minus n
x^2 (square) root x / the square root of x
x^3 cube root (of) x
x^4 fourth root (of) x
x^n nth root (of) x
(x+y)2 x plus y all squared
n! n factorial
x^x hat
x¯ x bar
x˜ x tilde
xi xi / x subscript i / x suffix i / x sub i
∑(i=1~n) ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
xthe norm (or modulus) of x
OAOA / vector OA
OA¯ OA / the length of the segment OA
AT A transpose / the transpose of A
A−1 A inverse / the inverse of A

5. Functions

f(x) fx / f of x / the function f of x
f:Sa function f from S to T
xx maps to y / x is sent (or mapped) to y
f’(x) f prime x / f dash x / the (first) derivative of f with respect to x
f”(x) f double-prime x / f double-dash x / the second derivative of f with respect to x
f”’(x) triple-prime x / f triple-dash x / the third derivative of f with respect to x
f (4) (x) f four x / the fourth derivative of f with respect to x
∂f/∂x1 the partial (derivative) of f with respect to x1
2f/∂x12 the second partial (derivative) of f with respect to x1
0 the integral from zero to infinity
limx0the limit as x approaches zero
limx0+the limit as x approaches zero from above
limx0−the limit as x approaches zero from below
logelog y to the base e / log to the base e of y / natural log (of) y
lnlog y to the base e / log to the base e of y / natural log (of) y
how can i read math set in English?
how to read math formulas in English? 

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