Precalc0001to0005-page10 - The statement “If p then q ”...

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(Section 0.2: Logic) 0.2.1 SECTION 0.2: LOGIC LEARNING OBJECTIVES • Be able to identify and use logical notation and terminology. • Understand the structure of an “if-then” statement. • Understand counterexamples and logical equivalence. • Know how to find the converse, inverse, and contrapositive of an “if-then” statement. • Understand necessary conditions and sufficient conditions. PART A: DISCUSSION • Although logic is a subject that is often relegated to discrete mathematics courses and courses in computer science and electrical engineering, its fundamentals are essential for clear and precise mathematical thought. PART B: PROPOSITIONS AND “IF-THEN” STATEMENTS A proposition is a statement that is either true or false. “If-Then” Statements
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Unformatted text preview: The statement “If p , then q ” can be written as “ p ± q .” • The proposition p is called the hypothesis ; it is an assumption or a condition . • The proposition q is called the conclusion . • If there are no cases where p is true and q is false, we say that the statement is true . • Otherwise, the statement is false , and any case where p is true and q is false is called a counterexample . If the statement is known to be true, we can write “ p ± q .” “ ± ” may be read as “ implies .” • Outside of True-False questions and the like, we generally assume that “if-then” statements given to us in textbooks are true. • WARNING 1 : “ ± ” denotes “approaches” when we discuss limits in calculus....
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