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EXAMPLE 3

Conjecture: Even integer Any integer = Even integer. EXAMPLE 3. Use inductive and deductive reasoning. ALGEBRA What conclusion can you make about the product of an even integer and any other integer?. SOLUTION. STEP 1.

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EXAMPLE 3

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  1. Conjecture: Even integer Any integer = Even integer EXAMPLE 3 Use inductive and deductive reasoning ALGEBRA What conclusion can you make about the product of an even integer and any other integer? SOLUTION STEP 1 Look: for a pattern in several examples. Use inductive reasoning to make a conjecture. (–2) (2) = –4, (–1) (2) =–2, 2 (2) = 4, 3 (2) = 6, (–1) (–4) = 4, = –12 (–2) (–4) = 8, 2 (–4) = –8, 3 (–4)

  2. ANSWER The product of an even integer and any integer is an even integer. EXAMPLE 3 Use inductive and deductive reasoning STEP 2 Let: nand meach be any integer. Use deductive reasoning to show the conjecture is true. 2nis an even integer because any integer multiplied by 2 is even. 2nmrepresents the product of an even integer and any integer m. 2nmis the product of 2 and an integer nm. So, 2nmis an even integer.

  3. Tell whether the statement is the result of inductive reasoning or deductive reasoning. Explain your choice. a. The northern elephant seal requires more strokes to surface the deeper it dives. b. The northern elephant seal uses more strokes to surface from 250 meters than from 60 meters. EXAMPLE 4 Reasoning from a graph

  4. a. Inductive reasoning, because it is based on a pattern in the data Deductive reasoning, because you are comparing values that are given on the graph b. EXAMPLE 4 Reasoning from a graph SOLUTION

  5. 5. Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true. Deductive reasoning: Let n be any integer. Use deductive reasoning to show the conjecture is true n + n = 2n  for Examples 3 and 4 GUIDED PRACTICE SOLUTION Conjecture: The sum of a number and itself is twice the number.

  6. 6. Use inductive reasoning to write another statement about the graph in Example 4. Then use deductive reasoning to write another statement. for Examples 3 and 4 GUIDED PRACTICE SOLUTION Using inductive reasoning: The more strokes it takes for the northern elephant to surface, the deeper it dove. Using deductive reasoning: The northern elephant seal uses fewer strokes to surface from 190 meters then from 410 meters.

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