1. LOGIC STATEMENTS
MARIELE BRUTAS
Ateneo de Naga University, Philippines

2. Statement
is a declarative sentence that
is either TRUE or FALSE.

3. Examples:


4. CONDITIONAL STATEMENTS
Conditional Statements are combinations
of statements in an If - then structure.
A statement in this form has two parts. The
phrase immediately following the word If is
the hypothesis and the phrase immediately
following the word then is the conclusion.

5. Identify the hypothesis and the conclusion
in each statement.
If it rains, then the ground is wet.
If a polygon is a nonagon, then it has 9 sides.
If an animal is a tiger, then it is a mammal.

6. Write each statement in its conditional form.
Dogs have four legs.
If an animal is a dog, then it has four legs.
Parallelograms have two pairs of parallel sides.
If a figure is a parallelogram, then it has two
pairs of parallel sides.
Parallel lines do not intersect.
If two lines are parallel, then they do not
intersect.

7. When is a conditional
statement true?
When is it false?

8. Statement: If I do my homework, then I get my
allowance.
I did my homework, and I got my allowance.
The hypothesis is true and the conclusion is true.
Answer: Since what was expected happened,
therefore the conditional statement is TRUE.

9. Statement: If I do my homework, then I get
my allowance.
I did not do my homework, and I did not get my
allowance.
The hypothesis is false, the conclusion is false.
Answer: Since it was not stated what will happen
if I do not do my homework, then the statement
cannot be false. Therefore it’s TRUE.

10. Statement: If I do my homework, then I get my
allowance.
I did not do my homework, I still got my
allowance.
The hypothesis is false, the conclusion is true.
Answer: Since it was not stated what will
happen if I do not do my homework, then the
statement cannot be false. Therefore it’s TRUE.

11. Statement: If I do my homework, then I get my
allowance.
I did my homework, but I did not get my
allowance.
The hypothesis is true, the conclusion is false.
Answer: Since the result is not what was
expected, therefore the statement is FALSE.

12. Summary:
Hypothesis
True
False
False
True
Conclusion
True
False
True
False
TRUE
TRUE
TRUE
FALSE

13. THEREFORE, a conditional statement
is false if you can give a case when the
hypothesis is true and the conclusion is
false.

14. When is each statement false given that the
hypothesis is true?
1. If LJ will rest for 10 days, then his ankle will heal.
LJ rests for 10 days, but his ankle still hurts.
2. If x is prime, then x is odd.
2 is prime but is not odd.
3. If I study, then I will pass the exam.
I studied but still failed the exam.