Transforming a Statement into an Equivalent If-then Statement

Direction: Tell whether the second statement is a valid consequence of the first   statement.

  1. Students who are studious will be successful someday.

                 Rosa is studious, then she will be successful someday.

  • Medical staff are infected by COVID-19.

                Mila is a nurse, then she is infected by COVID-19.

  • LSI and ROFW cannot enter Roxas City.

               Bert is from Taiwan, then he cannot enter Roxas City.

  • Students receive modules.

     Thessa is a student, then she receives modules.

  • Parallel lines do not intersect.

                 Lines A and B are parallel, then they do not intersect.

Answers:

Exercise 1

a. Valid

b. Not valid

c. Valid

d. Valid

e. Valid

Guide Questions

Write your answer on the space provided based on the activity above.

  • How can you say that the second statement is a valid consequence of the first    statement? not a valid consequence?

Valid if and only if it is necessary that if all of the premises are true, then the conclusion is true

Exercise 2

Direction:   Convert each statements to if- then statements and identify the hypothesis and the conclusion.

  1. An odd number is not divisible by 2.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

b. Collinear points are points on the same line.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

c. Prime numbers has exactly two distinct factors.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

d. A man from China is infected with CORONA VIRUS-19.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

e. A number that ends in 0 is divisible by 10.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

f. The sidewalk is wet. It rained last night

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

g. Vulnerable persons are prohibited to go out of their houses.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

h. Vertical angles are congruent.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

i. Rectangle has four sides.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

j. A Filipino lives in the Philippines.

If then: _____________________________________________________

Hypothesis: _____________________________________________________

Conclusion: _____________________________________________________

Answers:

Exercise 2

a. If- then statement:  If a number is odd then it is not divisible by 2,

   Hypothesis: A number is odd

   Conclusion: It is not divisible by 2

b. If- then statement:  If the points are collinear then they are on the same line,

   Hypothesis: The points are collinear

   Conclusion: They are on the same line

c. If- then statement:  If a number is prime then it has two distinct factors,

   Hypothesis:  A number is prime

   Conclusion: It has two distinct factors

d. If- then statement:  If a man is from China then he is infected with CORONA virus,

   Hypothesis: A man from China

   Conclusion: Infected with CORONA virus

e. If- then statement:  If a number ends in 0 then it is divisible by 10,

   Hypothesis: A number ends in 0

   Conclusion: Divisible by 10

f. If- then statement:  If the sidewalk is wet then it rained last night,

   Hypothesis: The sidewalk is wet

   Conclusion: It rained last night

g. If- then statement:  If the person is vulnerable then he is prohibited from going out of their house,

   Hypothesis: The person is vulnerable

   Conclusion: He is prohibited from going out of their houses

h. If- then statement:  If the angles are vertical then they are congruent,

   Hypothesis: The angles are vertical

   Conclusion: They are congruent

i. If- then statement:  If the figure is a rectangle then it has four sides,

   Hypothesis: The figure is a rectangle

   Conclusion: It has four sides

j. If- then statement:  If a man is a Filipino then he lives in the Philippines,

   Hypothesis: A man is a Filipino

   Conclusion: He lives in the Philippines

Guide Questions

  1. How do you transform statements into an if- then or conditional statements?

The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.

  • How do you identify a hypothesis? a conclusion?

The hypothesis of a conditional statement is the phrase immediately following the word if while conclusion of a conditional statement is the phrase immediately following the word then.

Exercise 3

Direction: Give 5 statements and transform into a conditional statement and identify the hypothesis and conclusion.

  1. Statement:         ____________­­­_____________________________________

           If-then statement:  ___________­­­______________________________________

           Hypothesis:           _________________________________________________

           Conclusion:           _________________________________________________

Ans:  

today is Friday, then tomorrow is Saturday.

Hypothesis: Today is Friday.

Conclusion: Tomorrow is Saturday.

  •  Statement:         ____________­­­_____________________________________

           If-then statement:  ___________­­­______________________________________

           Hypothesis:           _________________________________________________

 Conclusion:          _________________________________________________

Ans:

If two angles are supplementary, then the sum of the measures of the angles is180.

Hypothesis: Two angles are supplementary.

Conclusion: The sum of the measures of the angles is 180

  •  Statement:         ____________­­­_____________________________________

           If-then statement:  ___________­­­______________________________________

           Hypothesis:           _________________________________________________

 Conclusion:          _________________________________________________

Ans: If two lines form right angles, then the lines are perpendicular.

Hypothesis: Two lines form right angles

Conclusion: The lines are perpendicular.

  •  Statement:         ____________­­­_____________________________________

           If-then statement:  ___________­­­______________________________________

           Hypothesis:           _________________________________________________

 Conclusion:          _________________________________________________

Ans:

If 2x + 5 > 7, then x>1.

Hypothesis: 2x + 5 > 7

Conclusion: x > 1

  •  Statement:         ____________­­­_____________________________________

           If-then statement:  ___________­­­______________________________________

           Hypothesis:           _________________________________________________

 Conclusion:          _________________________________________________

Ans:

Sixteen-year-olds are eligible to drive.

Hypothesis: If you are sixteen years’ old

 Conclusion: then you are eligible to drive.

 V. Reflection

  1. What have you learned in the lesson?

Conclusion is the conclusion of a conditional statement is the result of the hypothesis while the hypothesis is the first, or “if,” part of a conditional statement.

  • How can you apply it to real-life situation/s? Cite an example.

In real life, the hypothesis is the first, or “if,” part of a conditional statement which means it is only an educated guess while the conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.

Image: Pexels

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