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B. Find a number that provides a counterexample to show that a given statement is false. 1. For all number x, x3 2x. 2. For all number x, 1621= x +1 (x-1) C. Use deductive reasoning to show that the following procedure always produces a number 5. Procedure: Pick a number. Add 4 to the number and multiply the sum by 3. Subtract 7 and then decrease this difference by the triple of the original number. D. Make a conjecture for each of the following Fibonacci sums, where F,. represents the nth Fibonacci number. a. Fn + 2Fn+1 + Fn+2 = ? b. Fn+ Fnti + Fn+3 = ? E. Answer the following Logical Puzzle questions and Solve a Logic Puzzle 1. Meena's mother has five daughters; Reene, Teena, Sheena, and Sheela. Who is the fifth daughter? 2. A woman had two girls who were born on the same hour of the same day of the same year. But they were not twins. How could this be so? 3. Each of the four friends Donna, Sarah, Nikkie and Shanelle has a four different pet (fish, cat, dog, and snake). From the following clues, determine the pet of each individual. a, Sarah is older than her friend who owns the cat and younger than her friend who owns the dog. b. Nikkie and her friend who owns the snake are both of the same age and the youngest members of their group. c. Donna is older than her friend who owns the fish. 4. "How many children do you have, and what are their ages?" ask the census taker. The mother answers, "I have three children. The product of their ages is 36, and the sum of their ages is the same as my house number." The census taker looks at the house number, thinks for a moment, and responds, "I'm sorry, but I need more information." "My oldest child likes chocolate ice cream," says the mother. "Thank you", replies the census taker. "I have all the information I require." How old are the children