Logic Chapter 2 Flashcards

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Questions and Answers

What is the converse of a conditional statement?

Negating the hypothesis and conclusion

Forming a biconditional

Switching the hypothesis and conclusion (correct)

Maintaining the same hypothesis and conclusion

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?

Whenever both parts have the same truth value Signup and view all the answers

What does the Law of Detachment state?

If the statement p -> q is true and p is true, then q is true. Signup and view all the answers

What is the Law of Syllogism?

If the statements p -> q and q -> r are true, then p -> r is true. Signup and view all the answers

What does the Addition Property state?

If equal quantities are added to equal quantities, the sums are equal. Signup and view all the answers

What is the Reflexive Property?

A quantity is congruent to itself. Signup and view all the answers

Describe the Substitution Property.

If x = y, then x can be substituted in for y in any equation. Signup and view all the answers

What does the Transitive Property state?

If a = b and b = c, then a = c. Signup and view all the answers

What is the Symmetric Property?

If a = b, then b = a. Signup and view all the answers

What does the Subtraction Property state?

If equal quantities are subtracted from equal quantities, the differences are equal. Signup and view all the answers

What is the Congruent Complements Theorem?

If two angles are complementary to the same angle, then they are congruent to each other. Signup and view all the answers

What does the Congruent Supplements Theorem state?

If two angles are supplementary to the same angle, then they are congruent to each other. Signup and view all the answers

What is the definition of the Linear Pair Postulate?

Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Signup and view all the answers

What does the Vertical Angles Theorem state?

If two angles are vertical angles, then they're congruent. Signup and view all the answers

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.