## 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