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set theory

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Prove A\[B intersection C]=[A\B]union [A\C]
using  venn diagram [de morgans law of set difference]
venn diagram for demorgan law of set
                  difference

venn diagram for demorgan law
For the L.H.S
first draw the venn diagram
for A , (B intersection C) 
 then draw the diagram for their difference
shown as (1)
For the R.H.S
draw the diagrams for (A\B) and (A\C)
use that to get the diagram of their union
shown as eqn(2)

since the diagrams show in (1) and (2)
are the same L.H.S = R.H.S.

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problem 2
let A ={0,1,2,3} and B={1,3,5,7,9}
let f:A-->B be a function given by
f(x)=2x+1. Represent this function as
a set of ordered pairs and as a table

f(x)=2x+1
f(0)=2*0+1=1
f(1)=2*1+1=3
f(2)=2*2+1=5
f(3)=2*3+1=7

Ordered pairs
f={(0,1),(1,3),(2,5),(3,7)}

table
x
0
1
2
3
f(x)
1
3
5
7


other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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