II.Write the following statements in symbolic form 2.The set of counting numbers from 1 to 10. 3.The set of positive odd numbers less than 15. 4.The set of integers from 1 to 10 that is divisible by 3. 5.The set of positive real numbers between 1 and 3.
II.Write the following statements in symbolic form
2.The set of counting numbers from 1 to 10.
3.The set of positive odd numbers less than 15.
4.The set of integers from 1 to 10 that is divisible by 3.
5.The set of positive real numbers between 1 and 3.
III.Enumeratethe elements of the following. Moreover, determine the cardinality of each set.
6.The set of prime numbers less than 25.
7.The set of letters in the word “integrity”.
8. {xlx is a three-digit positive even number}
9.{xlx ∈ Z and X^2= 25}
IV.Determine whether each of the following sets is finite, infinite, or null.
10.The set of the whole number between 5 and 6.
11.The set of points on a line segment.
12.The set of all odd numbers divisible by 2.
13.The set of even integers between 10 and 25.
V.Enumerate all the subsets of each of the following sets.
14. A = {l, o, v, e}
15. S = {w, o, r, l, d}
VII.Let A = {2, 4, 6, 8}, B = {6, 9}, C = {4, 8}. Answer each of the following questions. Justify your answers.
20.Is C ⊆ A?
21.Is B ⊆ A?
22.Is C ⊆ A?
23. Is B ⊆B?
VIII.State whether the following statements is true or false. Justify your answers.
24.{b}⊆{a, {b}, {c}}
25. b∈{a, b, c}
26.{b}∈{a, b, c}
27.b⊆{a, b, c}
28.{b}⊆{a, b, {c}}
IX. Let A = {a, b, c, d} and B = {x, y}.
29. Use the set-roster notation to write each of the following sets. Moreover, determine the cardinality of each set.
a.A x A
b.A x B
c.B x A
d.B x B
X.30. Which of the following sets are equal?
A = {x ∈ R l –2 < x < 2}
B = {x ∈ Z l –2 < x < 2}
C= {x∈ Z+ l–2 < x <2}
D = {0, 1, 2}
State whether or not the following relations are functions.
a.{(2,2), (4,4), (6,6)}_______________________________
b.{(5,3), (5,4), (5,5), (5,6)}_______________________________
c.{ (0,2), (3,-5), (0,4), (1,6)}_______________________________
d.{(x,y)/ y= 3x–8}_______________________________
e. {(x,y/y=x+3 over x-5}
2.Let the relation G be defined as {(1,2), (-1,2), (2,4), (3,8), (5, 12)}.
a.Write the domain and range of G.
b.Is G a function?
c.Draw a mapping diagram of G.
3.Let the relation H defined asH = {(x, y)ly= 3x2–3x+ 4}.
a.Write the domain and range of H.
b. Is H a function?
c. Draw a graph of H in the Cartesian plane.
4.Let the relation M defined M= {(x, y)ly= √x^2-49}
a. Write the domain and range of M.
b. Is M a function?
c. Draw a graph of Min the Cartesian plane.
5.Find three relation from {1, 2} to {6, 7} that are NOT functions.
6.a. Find all relations from {4, 5, 6} to {1, 2}.
b.Find all functions from {4, 5, 6} to {1, 2}.
c. What fraction of the relation from {4, 5, 6} to {1, 2} are functions?
7.Define a relation M from RtoRas follows: For all real numbers xand y, (x, y) ∈ M means that y^2= x. Is M a function? Justify your answer.
8.Determine whether the given sets are binary operations under addition, subtraction, multiplication, division and exponential. Justify your answer.
a. set of natural numbers
b. set of integers
c. set of rational numbers
d. set or real numbers
e. set of
9. If a∗b= 2a–3b+ 4ab, find the valuesof 5 ∗2and 3 2/5
10. If aob= a2+ 2band a∗b= b2–b, find (2*3) * 4.
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