Part 2 Math
Part 2 Math
Part 2 Math
Name:. DOMINGO, Paula Bianca Course/ Year & Section: BSHM 1-D
CHAPTER 2
MATHEMATICAL LANGUAGE AND SYMBOLS
SETS
Assessment.
1. True
2. True
3. False
4. False
5. False
6. Unit
7. Empty
8. Unit
9. Finite
10. Empty
11. Infinite
12. Unit
13. Empty
14. Finite
15. Finite
IV. Tell whether the following pair of sets are equal, equivalent, joint or disjoint.
III. U ={ 0,1, 2, 3, 4, 5, 6, 7, 8, 9 }
C ={ 0,1, 2, 3 , 4, 5
A ={2, 3, 4, 5 }
R ={ 4, 5, 6, 7 }
E ={ 6, 7, 8, 9 }
A. Determine whether each relation is a function or not. If it is not a function, tell why.
1. Not, False – Not all multiples of five are odd numbers, the only odd numbers that
multiples of five are : 5,15,25,35,and 45.
2. Proposition, True
3. Proposition, True
4. Not, False – Neither true nor false
5. Not, False – Imperative sentence
6. Proposition, True
7. Proposition, True
8. Proposition, True
9. Not, False - Neither true nor false
10. Proposition, True
B. Let p, q, r be the propositions. Write the following in symbols using the appropriate
connectives.
11. R ^ ¬Q
12. P^Q^R
13. ¬R↔P
14. P ¬Q ↔ R
15. P ↔Q ↔ R
C. Write the negation of the following.
21. Q ^p
22. R^S
23. ¬S ↔ p
24. P↔Q
25. ¬S ↔ p
1. ( p ↔ q) ^ (p ^ q)
p q ((p ↔ q) ∧ (p ∧ q))
F F F
F T F
T F F
T T T
2. ( p ↔ q)v (¬p ↔ ¬ q)
F F F
F T F
T F F
T T F
3. ( p ˅ ¬q ) ^ ( p ˅q )
((p ∧ ¬q) ∧ (p ∧
p q
q))
F F F
F T F
T F F
T T F
4. ( p ^ q ) ^ ( p ˅ q )
((p ∧ q) ∧ (p ∧
p q
q))
F F F
F T F
T F F
T T T
5. ( p ↔ q) → ( ¬p ↔ q)
F F F
F T T
T F T
T T F
Assessment
I. State the implication, converse, inverse and contrapositive of the following propositions.
⮚ Implication - If you review your lessons, then you will pass MMW.
⮚ Converse – If you do pass MMW, then you will review your lessons.
⮚ Inverse – If you do not review your lessons, then you will not pass MMW.
⮚ Contrapositive – If you do not pass MMW, then you will not review your
lessons.
2. Pae will attend the party only if Jest will accompany her.
⮚ Implication – If Pae attends the party, then Jest will accompany her.
⮚ Converse – If Jest accompanies her, then Pae will attend the party.
⮚ Inverse – If Pae does not attend the party, then Jest will not accompany her.
⮚ Contrapositive – If Jest does not accompany her, then Pae will not attend the
party.
Quantification
Assessment
MATHEMATICAL REASONING
Assessment
2n + 2n = 4n
4n = 2n { 4n = 2n }
2 2
The sum of any two even numbers is always an even counting number.
{ 2n is an even number}
12.The product of an odd counting number and an even counting number is always an even
counting number.
⮚ Odd number = 2n + 1
Even number = 2n
n is a integer
{ 2n + 1} 2n
{ 2n + 1 } 2n is even number
13.The sum of two odd counting numbers is always an odd counting number.
3 + 7 = 10 ( even )
7 + 11 = 18 ( even )
( 2n + 1 ) ( 2m + 1 ) = 4mn + 2 ( m + n ) +1
4mn + 2 ( m + n ) + 1 + 2 = 2mn + m + n + 1
Pick any counting number. Multiply by 6. Add 8 to the product. Divide the sum by 2.
Subtract 4 from the quotient.
⮚ Multiply 3 to 6.
⮚ Divide by 2 by 26.
Choose any counting number. Multiply the number by 8. Subtract 4 from the product.
Divide the difference by 2. Add 2 to the quotient. The resulting number is four times the original
number.
⮚ Multiply 1 to 8.
⮚ Divide by 4 by 2.
⮚ Add 2 making it 4.
⮚ Then when multiplied to the original number 1, we get the final answer of 4.
Chapter 3
PROBLEM SOLVING
Assessment.
1. A food committee prepared 3 kinds of sandwiches, 5 drinks, 4 fruits and three candies.
How many kinds of snacks containing a sandwich, a drink, a fruit and a candy are
possible?
⮚ There are 180 kinds of snacks containing a sandwich ,a drink, a fruit and a candy.
2. A survey on subjects being taken by 250 college students in Candon City revealed the
following information.
Subject Number of
students taking
the subject
Mathematics 145
Filipino 90
English 88
Math and Filipino 25
Filipino and English 38
Math and English 59
Math, Filipino and 15
English
How many took Math as their only subject? English only? Filipino only?
How many were taking Math and Filipino but not English?
How many were taking Filipino and English but not Math?
3. Four married couples are members of Couples of Christ. The wives names are Kathy,
Sally, Jovie and Apple. Their husbands are Danny, Wally, George and Fernando. Find out who is
married to whom.
⮚ George and Kathy
⮚ Dannie and Jovie
⮚ Wally and sally
⮚ Apple and Fernando
4. Christian can do a job in 6 hours. If he requests Boyet to work with him, the two can do the
job in 4 ½ hours. How long will it take Boyet to do the job alone?
6. Pepe, Juan and Jose deliver newspapers. Pepe delivers 3 times as many papers as Jose
and Juan delivers 13 more than Pepe. If the three children delivered 496 newspapers, how many
papers does each deliver?
7. A hat and a jacket cost P 1000. The jacket costs P900 more than the hat. What are the cost
of the hat and the cost of the jacket?
⮚ 21, 23, 25
9. Dan can do a piece of work in 8 days while Ed can do it in 24 days. How long will it take
them to do the work together?
10. Alfredo is 5 years older than Juan. How old are they now if in 8 years the sum of their ages
is 35.