Chapter5 Flashcards
Define a statement
A sentence that is either true or false, but not both
Define reasoning
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
Define conjunction
A statement in which two statements, p and q, are connected by and. The notation for the disjunction “p and q” is denoted by pAq
Define disjunction
A statement in which two statements, p and q, are denoted by or. The notation for the disjunction is “p or q” is denoted by pVq
Define conditional statement
A statement of the form “if p, then q” where p and q are statements. The notation for this conditional statement is p -> q.
Define bi conditional statement
A statement of the form “p if and only q” (symbolized pq), which means p->q and q->p
Define theorem 5.1
The conditional p-> q is equivalent to the disjunction ~p or q
Define converse of a conditional statement
It is obtained by switching the hypothesis and conclusion. The converse of p–>q is q–>p
Define the inverse of a conditional statement
It is obtained by negating both the hypothesis and conclusion. The inverse of p–>q is ~p–>~q
Define the contrapositive of a conditional statement
It is obtained by switching and negating the hypothesis and conclusion. The contrapositive of p–>q is ~q–>~p
Define theorem 5.2 contrapositive rule
A conditional statement is equal to its contrapositive. In other words, p–>q is equivalent to ~q–>~p
Define proof
A system of reasoning of argument to convince a person of the truth of a statement
Define inductive reasoning
An argument to establish that a statement is probably true
Define deductive reasoning
An argument to establish that a statement is absolutely certain
Define when an argument is valid
If the reasoning proceeds logically from the premises to the conclusion
Define when an argument is sound
If it is valid and all the premises are true
Define the law of deduction
A method of deductive proof with the following symbolic form p(assumed) q1 q2 qn(statements known to be true) r(deduced from statements above) p-->r(conclusion)
Define modus ponens
A method of deductive proof with the following symbolic form.
Premise 1: p–>q
Premise 2: p
Conclusion: q
Define modus tollens
A method of deductive proof with the following symbolic form.
Premise 1: p–>q
Premise 2: ~q
Conclusion: ~p
Define transitivity
A method of deductive proof with the following symbolic form:
Premise 1: p–>q
Premise 2: q–>r
Conclusion: p–>r
