Set theory question it , thank you

In summary, the question asks whether two statements are true or false in regards to sets A, B, and C within a universal set U. The first statement, A⊆B if and only if B'⊆A', is proven false with the use of two Venn diagrams. The second statement, If A∩C ⊆ B∩C then A⊆B, is proven true with a Venn diagram illustrating that the elements in set A are also in set B, making the statement true. The student is feeling stressed and has six more questions to complete by Monday.
  • #1
dhillon
14
0
set theory question please help it urgent, thank you

Homework Statement



1. Homework Statement

Let A, B and C be any sets inside our universal set U. Decide whether each of the following statements is true or false. Justify your answers by giving a proof or a counterexample as appropriate.

a) A⊆B if and only if B'⊆A'

b) If A∩C ⊆ B∩C then A⊆B

2. Homework Equations

X \ Y sets of elements in X but not Y. Y doesn't have to be a subset of X however if it is then X \ Y is the compliment of Y in X

3. The Attempt at a Solution

this is how i did it however i don't think its right hence i need your help thanks

a) with these 2 venn diagrams it shows that this statement is false as the elements don't have to be in set A or B , please see the attatched file for the diagrams , I am not sure please help thank you

b) With this venn diagram i think it shows the statement is true, this is as the set A has the the same elements that are also in set B therefore the statement is true. please help me out on this , see the attached document (i named the doc 2A for the first part n 2B for the second) thank you, please help
Attached Files



Homework Equations





The Attempt at a Solution

 
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  • #2


Nothing is attached.
 
  • #3


Nevermind...didn't see the other thread.
 
  • #4


thanks for the help, I am soo stressed with this and i got 6 other questions which I am still working on, I've done 9 and this is in for monday, please help, thanks
 

FAQ: Set theory question it , thank you

1. What is set theory?

Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects or elements. It provides a foundation for understanding concepts such as numbers, functions, and infinity.

2. What are the basic operations in set theory?

The basic operations in set theory include union, intersection, and complement. Union combines all the elements of two or more sets into one set. Intersection finds the common elements between two or more sets. Complement finds the elements that are in one set but not in another.

3. What is the difference between a set and a subset?

A set is a collection of elements, while a subset is a set that contains elements from another set. In other words, all the elements in a subset are also in the original set, but the original set may have additional elements.

4. How is set theory used in other fields of science?

Set theory has applications in many areas of science, including computer science, physics, and statistics. In computer science, it is used to build data structures and algorithms. In physics, it is used to study the properties of particles and their interactions. In statistics, it is used to analyze data and make predictions.

5. What are some famous paradoxes in set theory?

One famous paradox in set theory is Russell's paradox, which questions the existence of a set that contains all sets that do not contain themselves. Another paradox is the Banach-Tarski paradox, which states that it is possible to decompose a solid ball into a finite number of pieces and reassemble them to form two identical copies of the original ball.

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