Lesson 2 Flashcards
(25 cards)
What is a proposition?
A declarative statement that is either true or false, but not both.
Example: “The sky is blue.” (True or False)
What are non-propositions?
Questions, commands, or ambiguous statements that lack a clear truth value.
What is negation?
The opposite of a given proposition. If p is true, then ¬p is false.
What is conjunction?
The statement p∧q is true only if both p and q are true.
What is disjunction?
The statement p∨q is true if at least one of p or q is true.
What is a conditional statement?
“If p, then q.” True unless p is true and q is false.
What is a biconditional statement?
“p if and only if q.” True when both p and q have the same truth value.
What are truth tables used for?
Used to determine the truth values of compound propositions.
What is a tautology?
A statement that is always true regardless of the truth values of its components (e.g., p∨¬p).
What is a contradiction?
A statement that is always false (e.g., p∧¬p).
What is a contingency?
A statement that can be either true or false, depending on the truth values of its components.
What does implication mean?
p⇒q means if p is true, then q must also be true.
What is logical equivalence?
Two statements are logically equivalent if they have identical truth tables.
What is the definition of a set?
A collection of distinct objects, called elements.
What is the roster method?
Listing elements, e.g., A={1,2,3}.
What is set-builder notation?
Describing elements, e.g., B={x∣x is an even number}.
What is the union of sets?
The set of elements in either A or B or both.
What is the intersection of sets?
The set of elements common to both A and B.
What is the complement of a set?
The set of elements not in A.
What is the difference of sets?
The set of elements in A but not in B.
What are Venn diagrams used for?
Visual representation of sets and their relationships.
What is the commutative property?
A∪B=B∪A; A∩B=B∩A.
What is the associative property?
(A∪B)∪C=A∪(B∪C).
What is the distributive property?
A∩(B∪C)=(A∩B)∪(A∩C).
