Mathematics
Grade 10
15 min
Converses, inverses, and contrapositives
Converses, inverses, and contrapositives
What you'll learn
- Identify the place value of each digit in a decimal number to the hundredths place and write it in expanded form with 80% accuracy.
- Write decimals to the hundredths place in expanded form using fractions or decimals with 75% accuracy.
- Convert decimals written in expanded form (using fractions or decimals) back to standard form with 80% accuracy.
- Explain the relationship between the digits in a decimal number and its expanded form in your own words.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define conditional, converse, inverse, and contrapositive statements.
Write the converse, inverse, and contrapositive of a given conditional statement.
Translate conditional statements and their related forms into symbolic notation (e.g., p → q).
Determine the truth value of a conditional, converse, inverse, and contrapositive statement.
Identify the logical equivalence between a conditional statement and its contrapositive.
Identify the logical equivalence between the converse and the inverse of a statement.
If you get a 90% on the test, then you get an A. 🤔 Does that mean if you get an A, you must have scored 90%?
This lesson explores how to rearrange and modify 'if-then' statements to form their converse, inverse, and contrapositive. Unders...
2
Key Concepts & Vocabulary
TermDefinitionExample
Conditional StatementA logical statement with two parts, a hypothesis and a conclusion, typically written in 'if-then' form. It is the starting point for the other forms.If a polygon has three sides, then it is a triangle.
Hypothesis (p)The 'if' part of a conditional statement. It represents the condition or premise.In 'If it is raining, then the ground is wet,' the hypothesis is 'it is raining'.
Conclusion (q)The 'then' part of a conditional statement. It represents the result or outcome.In 'If it is raining, then the ground is wet,' the conclusion is 'the ground is wet'.
ConverseFormed by switching the hypothesis and the conclusion of the conditional statement.The converse of 'If a figure is...
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Core Formulas
Symbolic Forms of Logical Statements
Conditional: \(p \rightarrow q\)
Converse: \(q \rightarrow p\)
Inverse: \(\sim p \rightarrow \sim q\)
Contrapositive: \(\sim q \rightarrow \sim p\)
Use these symbols to represent the logical structure of statements. 'p' is the hypothesis, 'q' is the conclusion, '→' means 'implies' (if-then), and '~' means 'not' (negation).
The Law of Logical Equivalence
Conditional \(\equiv\) Contrapositive: \((p \rightarrow q) \equiv (\sim q \rightarrow \sim p)\)
Converse \(\equiv\) Inverse: \((q \rightarrow p) \equiv (\sim p \rightarrow \sim q)\)
A conditional statement is always logically equivalent to its contrapositive (they are either both true or both false). Similarly, the converse is alw...
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Sign Up Free to ContinueSample Practice Questions
Easy
In the conditional statement, 'If a polygon has three sides, then it is a triangle,' which part is the hypothesis (p)?
A.it is a triangle
B.a polygon has three sides
C.If a polygon
D.then it is a triangle
Easy
In the conditional statement, 'If it is raining, then the ground is wet,' which part is the conclusion (q)?
A.it is raining
B.If it is raining
C.then the ground
D.the ground is wet
Easy
Which logical statement is formed by swapping the hypothesis and the conclusion of a conditional statement?
A.Converse
B.Inverse
C.Contrapositive
D.Negation
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Frequently asked questions
What grade level is "Converses, inverses, and contrapositives"?
Converses, inverses, and contrapositives is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Converses, inverses, and contrapositives?
You'll be able to: Identify the place value of each digit in a decimal number to the hundredths place and write it in expanded form with 80% accuracy; Write decimals to the hundredths place in expanded form using fractions or decimals with 75%….
Is "Converses, inverses, and contrapositives" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Converses, inverses, and contrapositives?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.