Chapter 5 Flashcards
A statement is………
A sentence that is either true or false, but not both (5.2)
Reasoning is……..
The step-by-step process that begins with a known fact or assumption and builds to a conclusion in an orderly, concise way. This is also called logical thinking. (5.1)
Upside down A (universal quantifier)
All or every (5.2)
Backwards E (existential quantifier)
One or more; some (5.2)
A conjunction is ………
A statement in which two statements, p and q, are connected by “and”. The notation for the conjunction “p and q” is denoted by p^q (5.3)
A disjunction is….….
A statement in which two statements, p and q, are connected by “or”. The notation for the disjunction “p or q” is denoted by pVq (5.3)
A conditional statement is………
A statement of the form “if p, then q”, where p and q are statements . The notation for this conditional statement is p->q (5.4)
A biconditional statement is………
A statement of the form “p if and only if q” (symbolized by
pq), which means p->q and q->p.(5.4)
The converse of a conditional statement
is obtained by switching the hypothesis and conclusion. The converse of p->q is q->p. (5.4)
The inverse of a conditional statement
Is obtained by negating both the hypothesis and conclusion. The inverse of p->q is ~p->~q. (5.4)
The contrapositve of a conditional statement
is obtained by switching and negating the hypothesis and conclusion. The contrapositve of p->q is ~q->~p. (5.4)
A proof is ……
A system of reasoning or argument to convince a person of the truth of the statement (5.5)
Inductive reasoning is ………
An argument to establish that a statement is probably true (5.5)
Deductive reasoning is………
Is an argument to establish that a statement is absolutely certain (5.5)
An argument is valid if………
The reasoning proceeds logically from the premises to the conclusion (5.5)
An argument is sound if………
It is valid, and the premises are true (5.5)
The Law of Deduction is..……
A method of deductive proof with the following symbolic form:
p (assumed) qn (statements known to be true)
q1 r (decided from statements above)
q2 p->r (conclusion)
(5.6)
Modus ponens is…….
A method of deductive proof with the following symbolic form: Premise 1: p->q Premise 2: p Conclusion : q ( :. means therefore) (5.6)
Modus tollens is.……
A method deductive proof with the following symbolic form: Premise 1: p->q Premise 2:~q Conclusion:~p (5.6)
Transitivity is.……
A method of deductive proof with the following symbolic form: Premise 1: p->q Premise 2: q->r Conclusion:p->r (5.6)
