- #1
kathrynag
- 598
- 0
Homework Statement
Prove or disprove:
(A-B)'=B'-A'
Homework Equations
The Attempt at a Solution
Let x[tex]\in[/tex](A-B)'
Then x[tex]\notin[/tex](A-B)
I'm not sure where to go from here...
VeeEight said:A-B is the set of elements in A that are not in B
So x is not in A-B means that x is in A but is not in B
You may want to try to think of some counterexamples before trying to show inclusion both ways.
VeeEight said:If you are working in R, then the complement of the set A-B would be R - {1, 2, 5}
You might want to try some simpler examples like A= (0,1) or {1, 2, 3} and B = [0,1] or {3, 4}
kathrynag said:A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}
So, if x is not an element of A-B, then x is not an element of {1,2}VeeEight said:Okay.
Ok, sokathrynag said:Homework Statement
Prove or disprove:
(A-B)'=B'-A'
Homework Equations
The Attempt at a Solution
Let x[tex]\in[/tex](A-B)'
Then x[tex]\notin[/tex](A-B)
I'm not sure where to go from here...
kathrynag said:A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}
x[tex]\in[/tex]{3,4,5,6,7}kathrynag said:So, if x is not an element of A-B, then x is not an element of {1,2}
kathrynag said:A = {1,2,3} , B = {3,4} , universe = {1,2,3,4,5,6,7}
A-B = {1,2}
(A-B)' = {3,4,5,6,7}
kathrynag said:a={1,2,3}
b={3,4}
universe ={1,2,3,4,5,6,7}
a-b={1,2}
(a-b)'={3,4,5,6,7}
pizzasky said:keep going! What are a' , b' and b'-a' ?
This is an equation that represents the derivative of the function (a-b), which is equal to the derivative of b minus the derivative of a.
To solve for (a-b)'=b'-a', you can use the chain rule of differentiation. First, take the derivative of (a-b) which will give you 1. Then, take the derivative of b and a, and subtract them. This will give you the final answer of 1-b'.
Sure! Let's say that a = 2x and b = x^2. We can rewrite the equation as (2x-x^2)'=(x^2)'-2x'. Using the chain rule, we get 1-2x = 2x-2. Therefore, the final answer is 1-2x = 2x-2.
This equation is important in mathematics because it is used to find the rate of change of a function. The derivative of a function is a fundamental concept in calculus and is used in many applications such as physics, economics, and engineering.
Yes, there are many real-life applications of (a-b)'=b'-a'. For example, it can be used to calculate the velocity of an object in motion, the growth rate of a population, or the change in temperature over time. It is also used in optimization problems to find the maximum or minimum value of a function.