Note: The numbers 1, 2, 3, 4, 5, … are called counting numbers or natural numbers. Any counting number n divided by 2 produces a remainder of 0 or 1. If n÷2 has a remainder of 0, then n is an even counting number. If n÷2 has a remainder of 1, then n is an odd counting number. 1. The product of two odd counting numbers is always an odd counting number. 2. The sum of two odd counting numbers is always an odd counting number. 3. Pick any counting number. Multiply the number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice the original number. 4. Pick any number. Multiply the number by 8. Subtract 4 from the product. Divide the difference by 2. Add 2 to the quotient. The resulting number is four times the original number. find a number that provides a counterexample to show that the given statement is false. 5. For all numbers x, |x+3|=|x|+3. 6. For all numbers x, -x
Note: The numbers 1, 2, 3, 4, 5, … are called counting numbers or natural numbers. Any counting number n divided by 2 produces a remainder of 0 or 1. If n÷2 has a remainder of 0, then n is an even counting number. If n÷2 has a remainder of 1, then n is an odd counting number.
1. The product of two odd counting numbers is always an odd counting number.
2. The sum of two odd counting numbers is always an odd counting number.
3. Pick any counting number. Multiply the number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice the original number.
4. Pick any number. Multiply the number by 8. Subtract 4 from the product. Divide the difference by 2. Add 2 to the quotient. The resulting number is four times the original number.
find a number that provides a counterexample to show that the given statement is false.
5. For all numbers x, |x+3|=|x|+3.
6. For all numbers x, -x<x.
7. For all numbers x, |(x+1)(x-1)|(x-1)|=x+1.
8. Each four siblings (Anita, Tony, Maria, and Jose) is given 50,000 to invest in the stock market. Each chooses a different stock. One chooses a utility stock, another an automotive stock, another a technology stock, and the other an oil stock. From the following clues, determine which sibling bought which stock.
Clue 1: Anita and the owner of the utility stock purchased their share through online brokerage, whereas Tony and the owner of the automotive stock did not.
Clue 2: The gain in value of Maria’s stock is twice the gain in value of the automotive stock.
Clue 3: The technology stock is traded on NASDAQ, whereas the stock that Tony bought is traded on the New York Stock Exchange.
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