Worksheet: Analyzing Conditional Statements

In this worksheet, we will practice analyzing a given statement to identify hypothesis and conclusion to write it in if-then form; writing its converse, inverse, and contrapositive; constructing the conditional truth table; representing it using a Venn diagram; or identifying negations, conjunctions, and disjunctions.

Q1:

Read the following conditional statement: If it is raining, then Amelia has her umbrella up.

Write the converse of the statement.

  • AIf it is not raining, then Amelia does not have her umbrella up.
  • BIf Amelia does not have her umbrella up, then it is raining.
  • CIf Amelia does not have her umbrella up, then it is not raining.
  • DIf Amelia has her umbrella up, then it is raining.

Write the inverse of the statement.

  • AIf it is not raining, then Amelia has her umbrella up.
  • BIf it is not raining, then Amelia does not have her umbrella up.
  • CIf Amelia does not have her umbrella up, then it is raining.
  • DIf Amelia has her umbrella up, then it is raining.

Write the contrapositive of the statement.

  • AIf Amelia does not have her umbrella up, then it is raining.
  • BIf it is not raining, then Amelia does not have her umbrella up.
  • CIf Amelia has her umbrella up, then it is raining.
  • DIf Amelia does not have her umbrella up, then it is not raining.

Q2:

Read the following conditional statement: If Matthew does his homework, then he gets his weekly allowance.

What is the hypothesis?

  • AMatthew does his homework.
  • BMatthew gets his weekly allowance.

What is the conclusion?

  • AHe does his homework.
  • BHe gets his weekly allowance.

Q3:

Which of the following statements is true about the two planes?

  • AThe two planes are intersected.
  • BThe two planes are parallel.
  • CThe two planes are coincident.

Q4:

Complete using one of the choices below: If two planes have two common points 𝐴 and 𝐡, then they .

  • Aintersect at a straight line parallel to ⃖⃗𝐴𝐡
  • Bintersect at ⃖⃗𝐴𝐡
  • Chave a third point in common, which does not belong to ⃖⃗𝐴𝐡
  • Dare coincident

Q5:

Determine whether the following sentence is true or false: If 𝐴𝐡𝐢𝐷 is a quadrilateral, then there is only one plane passing through all of its sides.

  • Afalse
  • Btrue

Q6:

What does it mean for two lines to be considered skew?

  • AThey are not parallel.
  • BThey are located in the same plane.
  • CThey are not coincident.
  • DThey are not located in the same plane.

Q7:

Let 𝐴 be the hypothesis β€œπ‘₯+3=3+π‘₯” and 𝐡 be the conclusion β€œπ‘₯ is prime.”

The conditional statement 𝐴⇒𝐡 reads, β€œIf π‘₯+3=3+π‘₯, then π‘₯ is prime.” Is this true or false?

  • AFalse
  • BTrue

The converse statement 𝐡⇒𝐴 reads, β€œIf π‘₯ is prime, then π‘₯+3=3+π‘₯.” Is this true or false?

  • ATrue
  • BFalse

The inverse statement ¬𝐴⇒¬𝐡 reads, β€œIf π‘₯+3β‰ 3+π‘₯, then π‘₯ is not prime.” Is this true or false?

  • ATrue
  • BFalse

The contrapositive statement ¬𝐡⇒¬𝐴 reads, β€œIf π‘₯ is not prime, then π‘₯+3β‰ 3+π‘₯.” Is this true or false?

  • ATrue
  • BFalse

Q8:

Consider the conditional statement β€œIf 𝐴, then 𝐡,” where the hypothesis 𝐴 is β€œπ‘₯ and 𝑦 are even numbers” and the conclusion 𝐡 is β€œπ‘₯+𝑦 is even.”

Statement If 𝐴, then 𝐡. If 𝐡, then 𝐴. If not 𝐴, then not 𝐡. If not 𝐡, then not 𝐴.
True or False

Complete the table to give the truth value of the conditional statement and its converse, inverse, and contrapositive.

  • ATrue, True, False, True
  • BFalse, False, True, True
  • CFalse, False, False, True
  • DTrue, False, False, True
  • ETrue, False, False, False

Q9:

Which of the following is the inverse of the conditional statement β€œIf the measures of all the internal angles of a polygon are at most 180 degrees, then the polygon is convex?”

  • AIf a polygon is convex, then the measures of all the internal angles are at most 180 degrees.
  • BIf one of the internal angles of a polygon measures more than 180 degrees, then the polygon is not convex.
  • CIf a polygon is not convex, then one of its internal angles measures more than 180 degrees.

Q10:

Decide whether the conclusion is valid.

Given: If two angles in a triangle add up to 70 degrees, then the triangle is obtuse.

Given: 𝐴𝐡𝐢 is an obtuse triangle.

Conclusion: Two of the angles in triangle 𝐴𝐡𝐢 add up to 70 degrees.

  • AValid
  • BNot valid

Q11:

William knows that the following statement is true: If it rains today, the grass will be wet.

The grass was wet on Monday. Can you conclude that it rained on Monday?

  • AYes
  • BNo

It rained on Tuesday. Can you conclude that the grass was wet on Tuesday?

  • AYes
  • BNo

Q12:

Which of the following statements follows logically from statements A and B?

  1. If Liam misses the bus, then he will be late for work.
  2. If Liam is late for work, then he will not be paid a bonus.
  • AIf Liam was not paid a bonus, then he was late for work.
  • BIf Liam misses the bus, then he will not be paid a bonus.
  • CIf Liam is late for work, then he missed the bus.
  • DIf Liam was not paid a bonus, then he missed the bus.

Q13:

Hannah knows that the following two statements are true:

  • If a student does not complete their homework, they will get detention.
  • If a student gets detention, they will be late home.

Jacob got detention and was late home.

Can we conclude that he did not complete his homework?

  • ANo
  • BYes

Jennifer did not do her homework.

Can we conclude that she was late home?

  • AYes
  • BNo

Q14:

We can use Venn diagrams to model conditional statements.

Which Venn diagram models the following two statements?

  1. If an animal is a fish, then it lives in water.
  2. Dolphins live in water.
  • A
  • B
  • C
  • D

Use the Venn diagram to determine whether the following statement is valid:

All dolphins are fish.

  • ANot valid
  • BValid

Q15:

Consider the following Venn diagram.

Which conditional statement is represented by the diagram?

  • AIf a student got an A, then they scored over 90%.
  • BIf a student scored over 90%, then they got an A.

Use the Venn diagram to decide whether the following statement is valid: If Benjamin scored less than 90%, then he did not get an A.

  • ANot valid
  • BValid

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