tailieunhanh - Sat - MC Grawhill part 28

Tham khảo tài liệu 'sat - mc grawhill part 28', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 260 MCGRAW-HILL S SAT Lesson 7 Thinking Logically Numerical and Algebraic Proof Logical proofs aren t just for geometry class. They apply to arithmetic and algebra too. In arithmetic you often need to apply the laws of arithmetic such as odd X even even negative positive negative see Chapter 9 Lesson 3 to prove what you re looking for. When you solve an algebraic equation you use logical laws of equality such as the addition law of equality to prove the equation you want. Must Be True Questions Logic is especially useful in solving SAT must be true questions. You know them and hate them they usually have those roman numerals I II and III. To prove that a statement must be true apply the laws of equality or the laws of arithmetic. To prove that a statement doesn t have to be true just find one counterexample a valid example for which the statement is false. b - 1 is 6. The only positive integer pairs with a product of 6 are 2 X 3 and 1 X 6 so one possibility is that a 2 and b 4. This gives a b - 1 2 4 - 1 2 3 6 and it satisfies the condition that a b. Now check the statements. Statement I is true here because 4 2 2 which is an integer. Statement II is also true here because 4 is an even number. Statement III is also true because 2 X 4 8 which is 6 greater than 2. So the answer is E I II and III right Wrong. Remember that the question asks what must be true not just what can be true. We ve only shown that the statements can be true. We can prove that statement I must be true by testing all the possible cases. Since there is only one other possible solution that satisfies the conditions a 1 and b 7 and since 7 1 7 is an integer we can say with confidence that statement I must be true. But statement II doesn t have to be true because b can equal 7 which is not even. We have found a counterexample. Next we can prove that statement III must be true by checking both cases 2 X 4 is 6 greater than 2 and 1 X 7 is 6 greater than 1. We can prove it algebraically too If we add