Chapter 4 - Logic

Question 1

This is the study of the methods and principles used in distinguishing correct from incorrect arguments.

Answer 1

Logic

Question 2

Logic focuses on the _____ as opposed to the content of any
particular statement.

Answer 2

relationship among statements

Question 3

A set of proposition/s that provides
grounds or reasons for accepting
the conclusion.

Answer 3

Premise

Question 4

A proposition that is affirmed on the basis of the other propositions of the argument

Answer 4

Conclusion

Question 5

This is denoted by lower case letters such as p, q and r, is a sentence that is either true or false or has a truth value.

Answer 5

Proposition

Question 6

An argument is valid when the relationship of its premise and conclusion is such that it is _______ unless the conclusion is
___.

Answer 6

impossible for the premise to be true, also true

Question 7

When it is possible for the premise of an argument to be true but
its conclusion is false then the argument is _____.

Answer 7

invalid

Question 8

A conjunction is true if _______; otherwise, it is false.

Answer 8

both of its conjuncts are true

Question 9

A disjunction is true if _____; otherwise, it is false.

Answer 9

at least one of the disjuncts is true

Question 10

A disjunction will be false only when ______.

Answer 10

both of its disjuncts are false

Question 11

A conjunction will be false when ______.

Answer 11

at least one of its conjuncts is false

Question 12

some words used to indicate the conjunction include:

Answer 12

‘moreover’
‘furthermore’
‘but’
‘yet’
‘still’
‘however’
‘also’
‘nevertheless’
‘although’

Question 13

The negation of a true statement is ____ and the negation of a false statement is ____.

Answer 13

false, true

Question 14

The hierarchy of connectives is as follows: ____ first, then _____, then ____

Answer 14

~ first, then ∧, then ∨.

Question 15

This describes the truth-value of a compound proposition for each possible scenario.

Answer 15

Truth table

Question 16

A proposition that is true for all possible truth-values of its constituent propositions is called a _______.

Answer 16

tautology

Question 17

A proposition that is false for all possible truth-values of its constituent propositions is called a ____.

Answer 17

contradiction

Question 18

A proposition that is neither a tautology nor a contradiction is said to be a ______.

Answer 18

contingent

Question 19

If p and q are propositions, the compound proposition if p then q is called a______ (p implies q or implication of q by p) and is denoted by p→q.

Answer 19

conditional proposition

Question 20

In a conditional proposition p→q, the proposition p is called the ____ and the proposition q is called the _____

Answer 20

hypothesis (antecedent), conclusion (consequent)

Question 21

We say that P is a ______ for Q when it is impossible for Q to be false when P is true.

Answer 21

sufficient condition

Question 22

We say that P is a ______ for Q when it is impossible for Q to be true when P is false.

Answer 22

necessary condition

Question 23

What is the converse of p→q?

Answer 23

q →p

Question 24

What is the inverse of p→q?

Answer 24

~p→~q

Question 25

What is the contrapositive of p→q?

Answer 25

~q→~p

Question 26

The compound statement (p→q) ∧ (q→p) is called the ________

Answer 26

biconditional or equivalence proposition

Question 27

P and Q are said to be ______, denoted by P≡Q, if P and Q have the same truth-value for every possible choice of truth-values for the propositions involved in P and Q.

Answer 27

logically equivalent

Question 28

To prove that P and Q are logically equivalent, you can show that ___.

Answer 28

the biconditional proposition P↔Q is a tautology; that is, P is both necessary and sufficient for Q.

Question 29

Let P(x) be a statement involving the variable x and let D be a set. We call P(x) a ______ with respect to D

Answer 29

propositional function

Question 30

A propositional function P(x), by itself is neither ____.

Answer 30

true nor false