## MAT118 Review for Midterm I

1.1 Be able to analyze a syllogism with a Venn diagram. (Examples 2,3,4,
Exercises 3,5,9,11)
1.2 Understand the definition of "statement" and the use of the logical
connectives "and" "or" "not" and "implies". Be able to
translate a statement into a symbolic representation. (Examples 3,4,5,
Exercises 3,7,11,17)

1.3 Use truth tables to figure out under what circumstances a certain
statement is true (Examples 3,4). Understand what it means for two
statements to be equivalent, and be able to use truth tables to establish
equivalence of statements (Example 5). Understand de Morgan's laws:

- "not (A and B)" is equivalent to "(not A) or (not B)"
- "not (A or B)" is equivalent to "(not A) and (not B)"

(Exercises 7,9,23,35,43)
1.4 Understand the relation between a conditional and its
converse, inverse and contrapositive. Understand how to show
(using truth table, for example) that a conditional and its contrapositive
are equivalent, and that its converse and inverse are equivalent, but
that a conditional and its inverse are not equivalent (Example 3).
Understand that in "if A then B" A is "the premise" and B is " the
conclusion" (Example 4).
Understand "only if": "A only if B" is equivalent to "if A then B"
and understand that "A if and only if B" means "A implies B and
B implies A" (Example 5). (Exercises 7,13,21,27,35)

1.5 Be able to use a truth table to analyze an argument (Examples 1,3,4).
(Exercises 5,11,17,21).

Use the Chapter Review for further reviewing.

October 10 1999