The document outlines conditional statements and their corresponding logical forms, including hypothesis and conclusion, converse, inverse, and contrapositive. It emphasizes that a conditional statement and its contrapositive are always either both true or both false, and it discusses the equivalent nature of converse and inverse statements. Additionally, it provides examples of conditional statements and prompts for identifying logically equivalent statements.

2. CHECKING OF
ASSIGNMENT

3. Illustrate in Venn Diagram the
following conditional statements.
1. If three points are coplanar, they belong to the
same plane.
2. If you play violin, then you are a musician.
3. If frogs live in water, then they are
amphibians.
4. If two planes have no point in common, they
are parallel.
5. If you travel to another country, then you

4. CONDITIONAL
STATEMENTS
Logically Equivalent Statements

5. Lesson Objectives
•Identify the hypothesis and
conclusion of a conditional
statement
•Formulate the converse, inverse
and contrapositive of the if-then
statement
•Determine the logically equivalent

6. Read and analyze the
statements below.
Tell whether each
statement is true or
false.

7. •
animal is a bird, then it has
feathers.
•Converse: If an animal has
feathers, then it is a bird.
•Inverse: If an animal is not a
bird, then it has no feathers.
• Contrapositive: If an animal
has no feathers, then it is not a

8. Remember
•A conditional statement and
its contrapositive are either
both true or both false. The
original conditional statement
and its contrapositive will
always have the same
meaning.

9. •Similarly, the converse and
the inverse of a conditional
statement are either both
true or both false. The
converse and inverse of a
conditional statement will
always have the same
meaning.

10. •When two
statements are
both true or both
false, they are
called equivalent
statements.

11. Which of the following statements are logically
equivalent?
1. If you are a guitar player, then you are a
musician.
2. If you are a musician, then you are a
guitar player.
3. If you are not a guitar player, then you
are not a musician.
4. If you are not a musician, then you are
not a guitar player.

12. Give the equivalent
statement.
1. Conditional Statement: If I take out
my cell phone, then Ma’am Hazel will
confiscate it.
2. Conditional Statement: If I am happy,
then I smile.
3. Conditional Statement: If a triangle is
isosceles, then two of its sides are the
same.