PRACTICE PROBLEMS - VENN DIAGRAMS 2

QUESTION 1

The following information is given.
LaTeX: U=\left\{1,\:2,\:3,\:4,\:5,\:6,\:7,\:8,\:9,\:10\right\}

LaTeX: P={Prime Numbers}
LaTeX: Q={Odd Numbers}
Draw a Venn diagram to represent the information above.


QUESTION 2
LaTeX: S and LaTeX: T are subsets of the Universal set LaTeX: U such that:
LaTeX: U=\left\{k,\:l,\:m,\:p,\:q,\:r\right\}
LaTeX: S=\left\{k,\:l,\:m,\:p\right\}
LaTeX: T=\left\{k,\:p,\:q\right\}
(i) Draw a Venn diagram to represent this information
(ii) List, using set notation, the members of the set

(a) LaTeX: S\cup T
(b) LaTeX: S'


QUESTION 3

A Universal set, LaTeX: U, is defined asLaTeX: U=\left\{15,\:16,\:17,\:18,\:19,\:20,\:21,\:22,\:23,\:24,\:25\right\}
Sets LaTeX: M and LaTeX: N are subsets of LaTeX: U such that
LaTeX: M={Prime Numbers} and
LaTeX: N={Even Numbers}
(i) Draw a Venn diagram to represent the sets LaTeX: M, LaTeX: N and LaTeX: U.
(ii) List the elements of the set (M∪N)^'


QUESTION 4

The following information is given:
LaTeX: U=\left\{1,\:2,\:3,\:4,\:5,\:6,\:7,\:8,\:9,\:10\right\}
LaTeX: P=\left\{1,\:2,\:5,\:10\right\}
LaTeX: Q=\left\{2,\:3,\:5,\:8,\:9\right\}
LaTeX: P and LaTeX: Q are subsets of LaTeX: U, the Universal set.
(i) Draw a Venn diagram to represent the information above.
(ii) List, using set notation, the members of the set

(a) LaTeX: P\cap Q
(b) LaTeX: \left(P\cup Q\right)'


QUESTION 5
LaTeX: T and LaTeX: E are subsets of a Universal set, LaTeX: U, such that:
LaTeX: U=\left\{1,\:2,\:3,\:4,\:5,\:6,\:7,\:8,\:9,\:10,\:11,\:12\right\}
LaTeX: T={multiples of 3}
LaTeX: E={even numbers}
(i) Draw a Venn diagram to represent this information.
(ii) List the members of the set

(a) LaTeX: T\cap E
(b) LaTeX: \left(T\cup E\right)'


QUESTION 6
The Universal set, LaTeX: U, is given as
LaTeX: U=\left\{1,\:2,\:3,\:...,\:13,\:14,\:15\right\}
The sets LaTeX: A and LaTeX: B are subsets of LaTeX: U such that
LaTeX: A={Factors of 12}
LaTeX: B={Multiples of 3}
(i) List the members of the set LaTeX: A
(ii) List the members of the set LaTeX: B
(iii) Represent the sets, LaTeX: A, LaTeX: B and LaTeX: U on a Venn diagram.
(iv) List the members of LaTeX: \left(A\cup B\right)'.


QUESTION 7
The Venn diagram below shows the number of elements in each region.

Determine how many elements are in EACH of the following sets:
(i) LaTeX: A\cup B

(ii) LaTeX: A\cap B
(iii) LaTeX: \left(A\cap B\right)'


QUESTION 8

In the diagram above,
LaTeX: U={whole numbers less than 10}, and
LaTeX: A and LaTeX: B are subsets of LaTeX: U.
(i) Describe LaTeX: A and LaTeX: B in words.
(ii) List the members of LaTeX: A\cap B and describe the set, in words, in relation to LaTeX: A and LaTeX: B.
(iii) Determine LaTeX: n\left(A\cup B\right)'.