# Section 3.7: Review for Chapter 3

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 3.

And [3.1]
AND-gate [3.6]
Antecedent [3.2]
Argument [3.1]
Assuming the antecedent [3.4]
Assuming the consequent (fallacy) [3.4]
Because [3.3]
Biconditional [3.3]
Circuit [3.6]
Column [3.5]
Compound statement [3.1]
Conclusion [3.1]
Conditional [3.2]
Conjunction [3.1]
Connective [3.1]
Consequent [3.2]
Contrapositive [3.2]
Converse [3.2]
Counterexample [3.4]
Deductive reasoning [3.1]
De Morgan’s laws [3.3]
Denying the antecedent (fallacy) [3.4]
Denying the consequent [3.4]
Direct reasoning [3.4]
Disjunction [3.1]
Either … or [3.1]
Exclusive or [3.1]
Fallacy [3.4]
Fallacy of the converse [3.4]
Fallacy of the inverse [3.4]
False chain pattern [3.4]
Fundamental operators [3.6]
Fuzzy logic [3.1]
Gates [3.6]
Hypothesis [3.1]
Implication [3.3]
Inclusive or [3.1]
Indirect reasoning [3.4]
Invalid argument [3.1, 3.4]
Inverse [3.2]
Law of contraposition [3.2]
Law of detachment [3.4]
Law of double negation [3.2]
Law of the excluded middle [3.1]
Logic [3.1]
Logical equivalence [3.3]
Logical fallacy [3.4]
Modus ponens [3.4]
Modus tollens [3.4]
Negation [3.1]
Negation of a conditional [3.3]
Neither … nor [3.3]
No p is q [3.3]
Not [3.1]
NOT-gate [3.6]
Operator [3.1]
Or [3.1]
OR-gate [3.6]
Parallel circuit [3.6]
Postulates [3.4]
Premise [3.1]
Row [3.5]
Series circuit [3.6]
Simple statement [3.1]
Statement [3.1]
Syllogism [3.4]
Tautology [3.3]
Theorem [3.4]
Transitive reasoning [3.4]
Transitivity [3.4]
Truth set [3.3]
Truth table [3.2]
Truth value [3.2]
Unless [3.6]
Valid argument [3.1]

If you can describe the term, read on to the next one; if you cannot,
then look it up in the text (the section number is shown in brackets).

IMPORTANT IDEAS

Can you explain each of these important ideas in your own words?

Truth Table of Fundamental Operators [3.1, 3.2]

Law of Double Negation [3.2]

Law of Contraposition [3.2]

De Morgan’s Laws [3.3]

Negation of a Conditional [3.3]

Direct Reasoning [3.4]

Indirect Reasoning [3.4]

Transitive Reasoning [3.4]

Relationship Between Logic and Circuits [3.6]

Next, make sure you understand the types of problems in Chapter 3.

TYPES OF PROBLEMS

Determine whether a sentence is a statement. [3.1]
Find truth value of simple and compound statements. [3.1]
Write the negation of all, some, and not. [3.1]
Translate statements into symbolic form. [3.1-3.3]
Translate symbolic form into verbal statements. [3.2, 3.3]
Construct a truth table for a given symbolic form. [3.2]
Apply the definition of the conditional. [3.2]
Write the converse, inverse, and contrapositive for a given statement. [3.2]
Determine whether a given symbolic statement is true or false. [3.2]
Decide whether a given statement is a tautology. [3.3]
Write an implication as a disjunction. [3.3]
Write the negation of a compound statement. [3.3]
Reach conclusions when given certain real-life premises. [3.3, 3.4]

Be able to recognize, state, and prove valid forms of reasoning, namely direct reasoning, indirect reasoning, and transitive reasoning. [3.4]

Prove logical statements. [3.3, 3.4]
Determine whether a given argument is valid or invalid. [3.4]
Classify valid forms of reasoning and recognize common fallacies. [3.4]
Find a valid conclusion for a given argument. [3.4]
Classify items as an undefined term, defined term, postulate, or theorem. [3.5]
Prove simple theorems using given definitions and postulates. [3.5]
Solve logical puzzles. [3.5]
Design a circuit to simulate truth values of a given logical statement. [3.6]
Use gates to design a circuit. [3.6]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 3 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor.

Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you
missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.