Inductive and Deductive Reasoning in Mathematics in the Modern World, Assignments of Mathematics

Download Inductive and Deductive Reasoning in Mathematics in the Modern World and more Assignments Mathematics in PDF only on Docsity! Directions: Determine whether each of the following arguments is an example of inductive or deductive reasoning. Defend your answer by writing a concise explanation. 1. For the past 10 years, a tree has produced plums every other year. Last year the tree did not produce plums, so this year the tree will produce plums. Answer: The argument’s conclusion are based on specific examples where in the tree has created a pattern to produced plums every other year therefore, it is an example of inductive reasoning. 2. All home improvements cost more than the estimate. The contractor estimated that my home improvement will cost P35, 000.00. Thus my home improvement will cost more than P35, 000.00. Answer: Since the argument’s conclusion is a specific case of general assumption wherein it is stated that all home improvements cost more than the estimated amount which is P35, 000.00 therefore, the argument is an example of deductive reasoning. 3. All Nick Joaquin’s novels are worth reading. The novel The Woman with Two Navels is Nick Joaquin’s novel. Thus, The Woman with Two Navels is worth reading. Answer: The argument begins with the use of general premise “All Nick Joaquin’s novels are worth reading” that are certain by definition to reach the specific conclusion “The Woman with Two Navels is worth reading”, therefore it is an example of deductive reasoning. 4. Mang Kiko is a grandfather and he is bald. Therefore, all grandfathers are bald. Answer: The argument’s conclusion is mathematically true however the conclusion can also be questionable since “Mang Kiko is a grandfather and he is bald” is a premise while “all grandfathers are bald” is a faulty premise therefore, it is an example of inductive reasoning. Directions: Solve the given problems below. 1. A tsunami is a sea wave produced by an underwater earthquake. The height of a tsunami as it approaches land depends on the velocity of the tsunami. Use the table below and inductive reasoning to answer each of the following question: Velocity of tsunami, in feet per second Height of tsunami, in feet 6 4 9 9 12 16 15 25 18 36 21 49 24 64 a. What happens to the height of tsunami when its velocity is doubled? Answer: It is shown that when the tsunami’s velocity is doubled, it’s height quadrupled. b. What should be the height of tsunami if its velocity is 30 feet per second? Answer: With a velocity of 30 feet per second, a tsunami’s height will be increased to four times that of a tsunami with a speed of 15 feet per second. Therefore, a height of 4 multiplied by 25 will result in a tsunami that has a height of 100 feet with a velocity of 30 feet per second. 2. Consider the following procedure: Pick a number. Multiply the number by 9, add 15 to the product, divide the sum by 3, and subtract 5. Complete the above procedure for two distinct numbers. Use inductive reasoning to make a conjecture about the relationship between the size of the resulting number and the size of the original number. Answer: • Let 5, be the first original number, following the procedure stated above: Original number : 5 Multiply by 9 : 5 x 9 = 45 Add 15 : 45 + 15 = 60 Divide by 3 : 60 ÷ 3 = 20 Subtract by 5 : 20 - 5 = 15 • Let 7, be the first original number, following the procedure stated above: Original number : 7 Multiply by 9 : 7 x 9 = 63 Add 15 : 63 + 15 = 78 Divide by 3 : 78 ÷ 3 = 26 Subtract by 5 : 36 – 5 = 21 • Let 9, be the first original number, following the procedure stated above: Original number : 9 Multiply by 9 : 9 x 9 = 81 Add 15 : 81 + 15 = 96 Divide by 3 : 96 ÷ 3 = 32 Subtract by 5 : 32 – 5 = 27 Conjecture: Using the procedure stated above, the resulting numbers of the original numbers 5, 7, and 9, yield a number that is 3 times the original number.