Test 1. Determine the truth value of each of the following statement whether true or false. Write your answer after each of the statement.

1. Cebu is the queen city of the south.
-True
2. -8  -1.
-False
3. Lapulapu is our first national hero.
-True
4. 81 is a prime number.
-False
5. X > 10.
-False
6. 0 is a natural number.
-False
7. CCLEX is the new longest bridge in the Philippines.
-True
8. Manila is the capital of the Philippines.
-True
9. Whole numbers starts from 1.
- False
10. The conjunction is true if and only if both statements are true.
-True

1. All dogs are white.
- Some dogs are not white.
2. Some hen can’t lay eggs.
-All hen can lay eggs.
3. Some students play mobile legend.
-No students play mobile legend.
4. All vegetables are delicious.
- Some vegetables are not delicious.
5. All monkeys are not cute.
- Some monkeys are cute.
6. No dress are expensive.
- Some dress are expensive.
7. No government employee is good.
- Some government employee is good.
8. All people change.
- Some people don't change.
9. Some teacher are not good.
- All teacher are good.
10. Some country doesn't have pandemic.
-  All country does have pandemic.

Test 1. Identify if the following statement is true or false.
Write T if the statement is true and F if the statement is false. (2pts)

F  1. A statement that is always false is called tautology.
F 2. The conditional p→q is false if p is false and q is false. It is true in all other cases.
T 3. In negation, you only give its opposite value/statement.
F 4.The biconditional p q is true if p→q is true and q→p is false.
T 5. A tautology is a statement that is always true.

p    q     ~p    ~q
T    T      F      F
T    F      F      T
F    T      T      F
F    F      T      T


1.(p ↔q)vp

(p ↔q) |   v   |  p
    T       |   T   |   T
    F       |    T   |    T
    F       |   F   |    F   
    T       |   T   |   F

-Not Tautology

2.p→(p∧q)

p  |  →  |  p∧q
T   |    T  |    T   
T   |   F  |    F
F   |  T  |    F 
F   |  T  |     F

-Not Tautology

3.q∧(p v q)

 q   |  ∧   |  p v q
 T   |  T   |    T
 F   |   F   |    T
 T   |   T  |    T
 F   |   F   |     F

-Not Tautology

4.(~pvq)→p

~pvq  |  →  |  p
    T    |  T    |  T 
    F    |  T    |   T
    T    |  F    |   F 
    T    |  F    |   F

-Not Tautology

5.(qv~p) ↔ (~p∧~q)

qv~p  |  ↔  |  ~p ∧ ~q
 T     |    F     |      F   
  F     |    T     |      F
  T     |    F     |      F
  T     |    T     |      T

-Not Tautology