1. True or False: 1 point If inductive reasoning is done correctly, it results in conjectures that are guaranteed to be valid in all cases. True False OMG2. How many counterexamples are needed to Invalidate a conjecture that was written through inductive reasoning? 1 point A. None B. Only one C. At least two O D. No matter how many counterexamples you can find, they are not enough to invalidate a conjecture 3. Read the four possible conjectures below. Then, gather some evidence 1 point about the squares of the natural numbers, and choose the option which is supported by your evidence. Reminder: the natural numbers are just the "counting numbers" i.e. 1, 2, 3, 4,.. A. The square of a natural number will be odd B. The square of a natural number will be even C. The square of an odd natural number will be odd, and the square of an even O natural number will be even 29 Nowinvalidate a conjecture 3. Read the four possible conjectures below. Then, gather some evidence 1 point about the squares of the natural numbers, and choose the option which is supported by your evidence. Reminder: the natural numbers are just the 'counting numbers" i.e. 1, 2, 3, 4,... A. The square of a natural number will be odd O B. The square of a natural number will be even O C. The square of an odd natural number will be odd, and the square of an even natural number will be even O D. The square of an odd natural number will be even, and the square of an even natural number will be odd O Other: 4. Which of the four conjectures below is invalidated by the 1 point following counterexample: Cereal is usually eaten with a spoon. A. Soups are usually eaten with a spoon. 29 NovO G. The square of an odd natural number will be natural number will be even square of an event O D. The square of an odd natural number will be even, and the square of an even natural number will be odd O Other: 4. Which of the four conjectures below is invalidated by the 1 point following counterexample: Cereal is usually eaten with a spoon. A. Soups are usually eaten with a spoon. B. Cereal could be eaten with a fork. C. Any food usually eaten with a spoon must be a soup. D. Any food usually eaten with a spoon must be a breakfast food. 5. Which of the following is a counterexample that invalidates the following 1 point conjecture: When two natural numbers are squared, then added together, the result is always a perfect square. 29 Nov DO A Soups are usually eaten with a spoon. O B. Cereal could be eaten with a fork. O C. Any food usually eaten with a spoon must be a soup. O D. Any food usually eaten with a spoon must be a breakfast food. 5. Which of the following is a counterexample that invalidates the following 1 point conjecture: When two natural numbers are squared, then added together, the result is always a perfect square. A. 3 and 4 B. 4 and 5 O C. 6 and 8 D. 5 and 12 6. Sofia made the following conjecture: "The sum of two integers is always 1 point larger than either of the integers". Seth then gathered some evidence to test Sofia's conjecture, Seth's evidence is shown below. Choose the option that 29 Nov D D C A