Draw the Venn diagram to show the relationship of the four given sets in item number

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

MATH  ASSIGNMENT

A. Determine the truth value of the following statements: (1 pt each)

1. Baguio City is in Region 2 and Cebu City is Region VII.

2. Istanbul is the capital of Turkey or Melbourne is the capital of Australia.

3. If a number is divisible by 12, then it is divisible by 4.

4. The National Capital Region is composed of 17 cities.

5. Region 4A is composed of 6 provinces.

6. Quezon City is the largest city in the Philippines in terms of land area.

B. If p is a true statement and q and r are false statements, determine the truth value of the following: (1 pt each)

1. ~(p ^ q) v r

2. (p v ~q) ^ ~r

3 (p → q)↔ (~p →~r)

4. ~(p → q) v r

5. p ↔ (~q→ r)

6. ~[p ^ (q ↔ ~r)]

C. Construct a truth table for the following: (3 pts each)

1. (𝑝 → 𝑞) 𝖠 (~𝑝 → ~𝑞)

2. [𝑎 𝖠 (𝑏 ∨ 𝑐)] ↔ [(𝑎 𝖠 𝑏) ∨ 𝑐]

D. State the conditional, converse, inverse, and contrapositive of the statement: (4 pts)

“All odd numbers are not divisible by 2.”

E. Give the the negation of the following statements: (1 pt each)

1. Apple is a fruit or orange is not a vegetable.

2. Some Filipinos do not want to be vaccinated.

3. Some schools are open for face-to-face classes.

4. No student should be left behind.

G. Use Euler diagram to determine if the following arguments are valid or invalid: (3 pts each)

1. Some fruits are nutritious. Some nutritious food are expensive. Therefore, some fruits are expensive.

2. All athletes are physically fit. Some physical fit people are attractive. Therefore, some athletes are attractive. 

H. Exercise 5.2, number 4 p. 35 in the module (3 pts)

I. Exercise 5.2, number 5 p. 35-36 in the module (3 pts)

J. Refer to the table below describing the operation * on S = {e, a, s, y} (1 pt each))

1)   y * (e * s) = 

2)   ( s* a) *(y * e) = 

Do as indicated. Show all necessary solutions.

K. Write the following sets in Roster method: (1 pt each)

A = {x│x is a member country of the ASEAN}

B = {x│x is a planet in the solar system}

L. Write the following in Rule method: (1 pt each)

C = {Albay, Camarines Norte, Camarines Sur, Catanduanes, Masbate, Sorsogon}

D = { UP, UST, Ateneo, La Salle, Adamson, FEU, NU, UE}

M. Given the following sets:

𝑈 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

𝐴 = {𝑥│𝑥 is an odd number}

𝐵 = {𝑥│𝑥 is greater than or equal to 7}

𝐶 = {𝑥│𝑥 is less than 3}

Describe the following sets using the enumeration or roster method. (2 pts each)

1)  (𝐴 𝖴 𝐶)𝐶

2)  𝐶 \𝐵𝐶

3) 𝐴 ∩ (𝐵 𝖴 𝐶)

4) (𝐴 ∩ 𝐶)\𝐵𝐶

5) (𝐴 ∩ 𝐵) × 𝐶

N. Draw the Venn diagram to show the relationship of the four given sets in item number 3. (2 pts)

O. From a group of 100 freshmen, 60 play basketball, 50 play volleyball and 40 play football. Twenty-eight play basketball and volleyball, 24 play volleyball and football, 22 play basketball and football and 10 play all three sports. Draw a Venn diagram and answer the following questions: (4 pts)

1) How many freshmen play exactly two sports?

2) How many freshmen does not play any three sports mentioned?

Attachments:

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