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Step 2 List the possible combinations of truth values for p and q. Step 3 Use the truth values of p to determine the truth values of ~p. Step 4 Use the truth values of ~p and q to write the truth values for ~p q. Example 2: Construct a truth table for p (~q r).
2.2 Inductive and Deductive Reasoning with answers 7 Make a conjecture •Twelve geometry students were given a list of 50 words to memorize. The next day, each student had to list as many words as they could remember. The results are listed below. •Make a conjecture about based on the results.
Example 1 Write an equation for the nth term of the arithmetic sequence 2, 5, 8, 11, . . .. Then find a20. The first term is 2, and the common difference is 3. an a1 (n 1)d Equation for an arithmetic. + sequence. −. an 2 (n. − 1)3 Substitute 2 for a1 and 3 for d. = +. an 3n 1. = − Simplify. Use the equation to find the 20th term. an 3n.
Serafino · Geometry M T W R F 2C Proofs Practice – “Proofs Worksheet #2” 1. Given: O is the midpoint of MN Prove: OW = ON OM = OW Statement Reason 1. O is the midpoint of seg MN Given 2. Segment NO = Segment OM Def of midpoint 3.
Using the Law of Syllogism. If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements. If x2 > 25, then x2 > 20. If x > 5, then x2 > 25. If a polygon is regular, then all angles in the interior of the polygon are congruent.
In a two-column proof, each statement in the left-hand column is either given information or the result of applying a known property or fact to statements already made. Each reason in the right-hand column is the explanation for the corresponding statement.
Solve multistep linear equations. Identify and extend arithmetic and geometric sequences. Geometry: Write conditional and biconditional statements. Use inductive and deductive reasoning. Use properties of equality to justify steps in solving equations and to find segment lengths and angle measures.
