Manila Philippines
MATWRLD – Mathematics in the Modern World
2nd Term, SY 2021-2022
50
SEATWORK NO. 2
50
Name: Kealo Sebastian L. Sta Ana
Section:BFMM03
Term:2nd
Date: Feb 22, 2022
SY:2021-2022
Time:11:38 PM
A. Directions: Write the elements of the following sets using the set-roster notation.
Set
1. Set A is the set of months
in year.
Set-roster notation
A= {January, February, March, April, May, June, July, August,
September, October, November, December}
2. Set B is a set of integers
between -2 and 2.
B= {-1, 0, 1}
3. Set C contains the letters
in the word ‘mathematics’.
C= {m, a, t, h, e, i, c, s}
4. Set D is the list of towns in D= {Angono, Antipolo, Bagong Nayon, Baras, Binangonan,
the province of Rizal.
Cainta, Cardona, Cupang, Jala-Jala, Langhaya, Mambagat,
Mayamot, Montalban, Morong, Pilillia, San Mateo, Tanay,
Taytay, Teresa}
5. Set E is the set of even
E= {2}
prime numbers less than 20.
B. Directions: Write the elements of the following sets using the set-builder notation.
Set
Set-builder notation
F= {x∈W/10<x<25, x=3n}
6. Set F is the set of whole
numbers divisible by 3
between 10 and 25.
7. Set G is the set of real
number solution of x2 – 1= 0.
G= {x∈R/x 2 - 1 = 0}
8. H is the set of integers
between -2 and 2.
H= {x∈Z/-2<x<2}
9. I = { 2, 4, 6, 8, …}
I= {x∈W/x=2n}
10. J = {Tuesday, Thursday}
J={x=day that starts with T}
C. Directions: Write the elements of the following sets using the set-roster notation.
1. Given A = {3,5} and B ={0,2,4}. Let a relation R = A x B.
a. What are the elements of R? R= {0, 2, 3, 4, 5}
b. How many elements are in R? n(R)= 5
c. What are the domain? {3, 5}
d. What are the range? {0, 2, 4}
2. Find all relations from S= {1,2} to T = {4,5}. (1,4),(1,5),(2,4),(2,5)
3. Find all functions from R = {2,3} to S = {4,5}. (2,4)(3,5)
4. Let A = {1,2,3} and B ={6,8,10} and define a relation R from A to B as follows:
𝑦
For all (x,y) Є A x B, (x, y) Є R means that 𝑥 is an integer.
a. Is 2 R 8? Yes
b. Is 3 R 6? No
c. Is (3,10) Є R? Yes
d. Is (1,6) Є R? Yes
e. Write R as a set of ordered pairs. (1,6), (2,8), (3,10)
f. Write the domain and the range of R? D={1,2,3} , R={6,8,10}
g. Draw an arrow diagram for R.
1
6
2
8
3
10
5. Define a relation S from R to R as follows:
For all (x,y) Є R x R, (x,y) Є S means that x > y.
a. Is (2,1) Є S? Yes
b. Is (2,2) Є S? Yes
c. Is 2 S 3? No
d. Is (-1) S (-2)? No
e. Give an example of the set with at least three elements satisfying the said
condition. (3,0), (4,2), (5,4)
6. A binary operation is defined one the set {1,2,3,4}. The table shows the
16 possible answers using this operation.
a. What is 2 * 4? 2
b. What is 3 * 2? 4
c. Is * commutative? Explain. Yes, for example, 2*3=3*2, so 4=4.
d. Is * associative? Explain. If 2*(3*4)= (2*3)*4
2*3 = 4*4
4=4
Yes, it is associative.
e. Is there identity element in *? Yes
7. Let the binary operation *, be defined as a * b = a + 2b, where a and b are real numbers.
a. What is 2 * 3? a + 2b = 2 + 2(3) = 2 + 6 = 8
b. Is * commutative? No
c. Is * associative? No