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1. JOMER JOHN V. ALVARADO
BSAIS-I
SEMI- FINAL
Exercise set 5.1
1. Statement of fact
ANSWER: Star Wars: The Force Awakens the gretest movie of all time.
3. Statement of fact
ANSWER: Harvey Mudd college is in Oregon
5. Question
ANSWER: Do you like to read?
7.Statement of fact
ANSWER: The area code for Storm Lake,Iowa , is 512
9. x = -5
ANSWER:
11. The principal will attend the class on Tuesday and Wednesday.
ANSWER: If today is Wednesday ( w ), the tomorrow is Thursday ( t )
13. A triangle is an acute triangle then it has three acute angles.
ANSWER: A triangle is an acute triangle if and only if it has three acute angles.
15. The Giant did not lost the game.
ANSWER: The Giants lost the game

2. Exercise 5.2
1. The truth value of this compound statement is False.
3. The truth value of this compound statement is True.
5. The truth value of this compound statement is True.
7. The truth value of this compound statement is False.
9. The truth value of this compound statement is False.
11. a. p˅ (q ᶺ r)
p ˅ (q ᶺ r)
p ˅ p
p
B. Because the p and q are the true statement and the r is false
statement.
13.
~p q ~p ˅ q
F T F T T
T F T T F
F T F T T
F F T T F
15.
P ~ q P ᶺ ~ q
T F T F F
T F T T T
F F F F F
F T F F T

3. Exercise 5.3
1.Antecedent: If I had the money
Consequent: I would buy the painting
3. Antecedent: If they had a guard dog
Consequent: No one would trespass on their property
5. Antecedent: If I change my major
Consequent: I must reapply for admission
7.Both given statement is true because this are even integer.
9. Both given statement is true statement.
11. If 4 < 3 is a true statement and the second is false statement. So, thus given
statement is false statement.
13.Both given statement is true statement.
15.
P Q ( P ^ ~ q) → [ ~ ( p ^ q)
T T T F F T T T T T
T F T F T F T T F F
F T F F F F F F F T
F F F F F T F F T F
17.
P Q [ (p → q) ^ p] → q
T T T T T
T F T T T
F T F T T
F F F F F

4. 19.
21.
P Q r [ (p → q ) ˅ (r ^ ~p ] → (r ˅ ~q
T T T T T T T T F F T T T F
T T F T T T T F F T T F T T
T F T T T F T T F F T T T F
T F F T T F F F F T T F T T
F T T F T T T T F F T T T F
F T F F T T T F F T T F T T
F F T F F F T T F F T T T F
F F F F F F F F F T T F T T
P Q R [ ( r ^ ( ~p ˅ q )] → ( r ˅ ~q)
T T T T T T T T T T T F
T T F F F T T F T F T T
T F T T T T T T T T T F
T F F F F T T F T F T T
F T T T F F T T T T T F
F T F F F F F F F F T T
F F T T F F T T T T T F
F F F F F F F F F F T T

5. 23.
Exercise 5.4
1. If we can take the aerobics class then we will be in good shape for the ski trip.
3. A number is an odd prime number if and only it is greater than 2.
5.If he has a talent to play keyboard then he join the band.
7. if I will be able to prepare for the rest then I have the textbook
P Q R [~ (p → ~ r) ^ ~q ] → r
T T T T T T F F F T T
T T F T T T T T T T F
T F T T T T F F F T T
T F F T T T T T T T F
F T T T F T F F F T T
F T F T F T T T T T F
F T T F F F F F F T T
F T F T F T T T T T F

6. 9.If running the Boston marathon then being in excellent shape necessary condition.
11. Converse: if I would quit this job then I were rich.
Inverse: if I do not were a rich then I will not quit this job.
Contrapositive: if I do not quit this job then I did not were rich
13. Converse: if I would not able to attend the party then she does not return soon.
Inverse: if she does not return soon then I would not able to attend the party.
Contrapositive: if I do not able to attend the party then she did not return soon.
15. Converse: If a figure is a parallelogram, then it is not a quadrilateral.
Inverse: If a figure is not a quadrilateral, then it is a parallelogram.
Contrapositive: If a figure is a quadrilateral, then it is a parallelogram
17. Converse: if I would access to the internet then I able to to get current information about
astronomy
Inverse: if I would be able to get current information about astronomy then i will not access to
the internet.
Contrapositive: if I do not access to the internet then I did not able to get current
information about astronomy.
19. Converse: if we would take a taxi then we will not have enough money for dinner.
Inverse: if we do not have enough money for a dinner then we will not take a taxi.
Contrapositive: if we do not take a taxi then we did have enough money for a dinner.

7. 21.Converse: if she would can extend her vacation for at least two days then she will not visit
Kauai.
Inverse: if she do not visit Kauai then she will not can extend her vacation for at least two
days.
Contrapositive: if she do not can extend her vacation for at least two days then she did not
visit Kauai.
23. Converse: Two lines given line a parallel, then line are perpendicular.
Inverse: two lines are not perpendicular, then given line not parallel.
Contrapositive: two lines do not parallel, then lines not perpendicular.
25. if the second statement is the converse of the first. The statements are not equipment.
27. if the second statement is the converse of the first. The statements are not equipment.
29.The second statement is the contrapositive of the first. The statement are equivalent.

8. Exercise set 5.5
1.
3.
5.
7.
9.

9. 11.
P ~~q P → ~ q ~q ~q
T F T F F
T T F T T
F F T F F
F T F T T
13.
~p ~q ~p → ~ q ~q ~ p
F F T F F
T T F T T
F F T F F
T T F T T
15.
P Q ( p→ q) ^ ( ~p →q)
T T F T T
T F T T F
F T F T T
F F T T F
P Q P ˅ ~q ~q ~q
T T T F F
T F T T T
F T T F F
F F F T T