Chapter 2 Terms Flashcards
Conditional Statement
A conditional statement is a logical statement that has 2 parts, a hypothesis (p) and a conclusion (q). When a conditional statement is written in if-then form, the “if” part contains the hypothesis and the “then” part contains the conclusion
If p, then q
Negation
The negation of a statement is the opposite of the original statement. To write the negation of statement p, you write the symbol for negation (~) before the letter
~p
Converse
To write the converse of a conditional statement, exchange the hypothesis and the conclusion
If q, then p
Inverse
To write the inverse of a conditional statement, negate both the hypothesis and the conclusion
If not p, then not q
Contrapositive
To write the contrapositive of a conditional statement, first write the converse, then negate both the hypothesis and the conclusion
If not q, then not p
Biconditional Statement
When a conditional statement and its converse are both true, you can write them as a single biconditional statement. A biconditional statement is a statement that contains the phrase “if and only if”
p if and only if q
Inductive Reasoning
A conjecture is an unproven statement that is based on observations
Counterexample
To show that a conjecture is true, you must show that it is true for all cases. You can show that a conjecture is false, however, by finding just one counterexample. A counterexample is a specific case for which the conjecture is false.
Deductive Reasoning
Deductive reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument. This is different from inductive reasoning, which uses specific examples and patterns to form a conjecture.
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Reflexive Property
a = a
Symmetric Property
If a = b, then b = a
