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Make a venn diagram Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.
- Let p and q be the propositions. (50 points)
p: It is below freezing.
q: It is snowing.
Express each of these propositions in complete English sentences.
a) p ∧ q (7 points)
b) p ∧ ¬q (7 points)
c) ¬p ∧ ¬q (7 points)
d) q ∨ p (7 points)
e) p → q (7 points)
f) q ∧ ¬p (7 points)
g) q → p (8 points)
2. Solve the following. (50 points)
a) Construct a truth table. (10 points)
¬p ∧ ( p ↔ ¬q )
b) Construct a truth table. (10 points)
p → ( q ∧ r )
c) Construct a truth table. (10 points)
( p → q ) ∨ ( ¬p ↔ r )
d) Find out if the following is a tautology, contradiction, or contingency. (10 points)
( p ∨ q ) ∧ ( ¬p ∧ ¬q )
e) Find out if the following propositions have logical equivalence. (10 points)
( p ↔ q ) ≡ ( p → q ) ∧ ( q → p )
There are 7 boys and 5 girls in a youngsters’ club. A committee of 3 boys and 2 girls is to be chosen. How many different possibilities are there?
How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?
Student , Height , X²
Hazel Kim , 1.47 , 2.16
Mee Ann Mae , 1.58 , 2.50
Grace Ann , 1.67 , 2.79
Jethro , 1.69 , 2.86
Chelsea Mae , 1.51 , 2.28
TOTAL: 9.92 , 12.59
1. Solve for the mean of the population μ.
2. Solve for the mean of the sampling distribution of the sample means Hr.
3. Compare u and ur.
4. Solve for the variance (a) and the standard deviation (a) of the population.
5. Solve the variance (or) and the standard deviation (ar) of the sampling distribution of the sample means Hr.
6. Compare a and or.
The SSG President wants to determine the weekly allowance of the Grade 11 students. A sample of 60 students were
surveyed. The sample is normally distributed with σ=19.5.
The SSG President wants to determine the weekly allowance of the Grade 11 students. A sample of 60 students were
surveyed. The sample is normally distributed with σ=19.5.
B.Caridad is a Product Manager receiving an annual salary of P118,000.00 She receives commission on her own sales of 1% and an override of of 1% on her men's sales. She sold P128,560.00 for the past month. Her men all receive a basic pay of P7,860.00 a month and a commission of 2% on their respective sales plus bonus of 14% on all sales exceeding P200,000.00. Her men's sales are as follows: F. Sta. Cruz, P125 230.00; A. Tante, P96 975.00; M. Umali, P239,100.00 and E. Inocencio, P108,675.00. The company deducts SSS contributions of 3.63% and PhilHealth contributions of P100.00 and 1% for Withholding tax. Compute for.
a.Gross earnings of B. Caridad
b. Net pay of B. Caridad
C. Gross earnings of each of the salesmen
d. Use Excel to incorporate (a) and (b).
3.Helen receives a monthly salary of P18 800.00. Compute for her:
a.annual salary
b. weekly salary
c.daily rate for 5-day week
d. semi-monthly salary
e.bi-weekly salary
f. hourly rate for 40-hour week
A professor only gives two types of exams, "easy" and "difficult". you will
get a difficult exam with a probability of 0.80. The probability that the first question
on the exam will be marked as difficult is 0.90 if the exam is difficult and 0.15 otherwise.
What is the probability that the first question on your exam is marked as difficult. How many
the probability that your exam is difficult to remember the first question on the exam is marked as
difficult?For each binary operation ∗ defined below say whether the following is
a group or not
a) Define ∗ 𝑜𝑛 𝑍 by 𝑎 ∗ 𝑏 = 𝑎 − 𝑏
b) Define ∗ 𝑜𝑛 𝑍 by 𝑎 ∗ 𝑏 = 𝑎𝑏
c) Define ∗ 𝑜𝑛 𝑅+by 𝑎 ∗ 𝑏 = 𝑎𝑏
d) Define ∗ 𝑜𝑛 𝑄 by 𝑎 ∗ 𝑏 = 𝑎𝑏
#339914 on Dec 2023