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Venn diagram

by shohruh
(kuala lumpur,malaysia)

Venn Diagram

Venn Diagram











































Given the following universal set U and its two subsets P and Q,
U = {x: x is an integer, 0 x 10}
P = {x: x is prime number}
Q = {x: x2 < 60}
(a) Draw a Venn diagram for the above sets.
(b) List the element in P’ Q.
(c) Find n(P’)

Comments for Venn diagram

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Feb 16, 2011
Venn Diagram
by: Staff

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Part II

(b) List the elements in P’ Q.

The universal complement of set P in set Q. This could also be written: P’ \ Q, or P’ - Q

P’ ("P-prime"), the universal complement of set P, is the set of all elements of set U which are not elements of set P.

P’ = set U without any of the prime numbers in set P

P’ - Venn Diagram (click link to view):

http://www.solving-math-problems.com/images/Venn-Diagram-Set-P-prime.png




P’ – Q, or P’ \ Q = set of elements in set P’ which are not elements of set Q
Venn Diagram (click link to view)

http://www.solving-math-problems.com/images/Venn-Diagram-Set-P-prime-minus-Q.png



(c) Find n(P’)

n(P’) the number of elements in the universal complement of set P

U = {1,2,3,4,5 … 98,99,100}
Set U has exactly 100 elements


P = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}
Set P has exactly 25 elements


Therefore, P’ has exactly 75 elements.




Thanks for writing.


Staff
www.solving-math-problems.com


Feb 16, 2011
Venn Diagram
by: Staff

The question:
Given the following universal set U and its two subsets P and Q,
U = {x: x is an integer, 0 x 10}
P = {x: x is prime number}
Q = {x: x2 < 60}
(a) Draw a Venn diagram for the above sets.
(b) List the element in P’ Q.
(c) Find n(P’)



The answer:

Part I

(a) Draw a Venn diagram for the above sets.

It is unclear about what elements are contained in each set.

-------------------
Universal Set U.

Does “0 x 10” mean that x can only have the values between 0 and 10? If that is true then the universal set would have a smaller number of elements than either of its subsets: P or Q. I assume you left off a 0, so that x can actually have a value between 0 and 100.

Assuming that is the case:

U = {x: x is an integer, 0 ≤ x ≤100}

-------------------
Set P.

Does “x is prime number” mean all prime numbers? If that is true then set P will have more elements than set U, which is impossible. There must be some limit on the number of elements in set P. For the sake of argument, I’m going to arbitrarily confine the values in set P to prime numbers between 1 and 100.

P = {x: x is prime number, 1 < x ≤100}

-------------------
Set Q.

Did you intend “x < 60” to include negative integers? If that is true then set Q will have more elements than set U, which is impossible. For the sake of argument, I’m going to arbitrarily confine the values in set P to prime numbers between 1 and 60.

Q = {x: x is an integer, 1 < x < 60}

-------------------
If these changes are made, then:

U = {x: x is an integer, 0 ≤ x ≤100}
P = {x: x is prime number, 1 < x ≤100}
Q = {x: x is an integer, 1 < x < 60}

Each set contains the following elements:

U = {1,2,3,4,5 … 98,99,100}
P = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}
Q = {2,3,4,5 … 57,58,59}



Set P - Venn Diagram (click link to view):
P = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}

http://www.solving-math-problems.com/images/Venn-Diagram-Set-P.png



Set Q - Venn Diagram (click link to view):
Q = {2,3,4,5 … 57,58,59}

http://www.solving-math-problems.com/images/Venn-Diagram-Set-Q.png


Set U - Venn Diagram (click link to view):
U = {1,2,3,4,5 … 98,99,100}

http://www.solving-math-problems.com/images/Venn-Diagram-Set-U.png



the INTERSECTION of sets P & Q, P∩Q - Venn Diagram (click link to view):
P∩Q = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59}

http://www.solving-math-problems.com/images/Venn-Diagram-Intersection-P-Q.png



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