Questions and Answers
What is the converse of a conditional statement?
What is the definition of the inverse?
Formed by negating the hypothesis and negating the conclusion of the original statement.
What does the contrapositive involve?
Switching the hypothesis and conclusion and negating both.
When is a biconditional true?
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What does the Law of Detachment state?
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What is the Law of Syllogism?
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What does the Addition Property state?
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What is the Reflexive Property?
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Describe the Substitution Property.
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What does the Transitive Property state?
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What is the Symmetric Property?
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What does the Subtraction Property state?
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What is the Congruent Complements Theorem?
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What does the Congruent Supplements Theorem state?
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What is the definition of the Linear Pair Postulate?
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What does the Vertical Angles Theorem state?
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Study Notes
Converse, Inverse, and Contrapositive
- Converse: Results from switching the hypothesis and conclusion of a conditional statement; represented as q -> p.
- Inverse: Formed by negating both the hypothesis and conclusion of the original statement; represented as ~p -> ~q.
- Contrapositive: Involves switching and negating both the hypothesis and conclusion of a conditional statement; represented as ~q -> ~p.
Biconditional and Logical Theorems
- Biconditional: True when both parts share the same truth value, expressed as "p if and only if q"; connects hypothesis p and conclusion q.
- Law of Detachment: States if p -> q is true and p holds true, then q must also be true.
- Law of Syllogism: If p -> q and q -> r are true, it can be concluded that p -> r is also true.
Properties of Equality
- Addition Property: If equal quantities are added to equal quantities, the resulting sums remain equal.
- Reflexive Property: A quantity is always congruent to itself, denoted as a = a.
- Substitution Property: Allows substitution in equations; if x = y, x can replace y in any equation, and vice versa.
- Transitive Property: Establishes that if a = b and b = c, then a must equal c.
- Symmetric Property: Indicates that if a = b, then it follows that b = a.
- Subtraction Property: If equal quantities are subtracted from equal quantities, the outcomes will remain equal.
Angle Theorems and Properties
- Congruent Complements Theorem: States that if two angles are complementary to the same angle, they are congruent to each other.
- Congruent Supplements Theorem: If two angles are supplementary to the same angle, they are congruent to each other.
- Linear Pair Postulate: Defines a linear pair as two adjacent angles whose non-shared rays form a straight line.
- Vertical Angles Theorem: Establishes that if two angles are vertical, they are congruent to each other.
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Description
Explore essential concepts in logic with flashcards covering Converse, Inverse, and Contrapositive statements. Learn the definitions and theorems that form the foundation of logical reasoning. Ideal for students seeking to enhance their understanding of conditional statements.
