LESSON 3: Problem Solving and Reasoning

Problem Solving and Reasoning

Inductive Reasoning 

        The type of reasoning that forms a conclusion based on the examination of specific examples is called inductive reasoning. The conclusion formed by using inductive reasoning is often called a conjecture, since it may or may not be correct. When you examine a list of numbers and predict the next number in the list according to some pattern you have observed, you are using inductive reasoning.

Deductive Reasoning 

Deductive reasoning is the process of reaching a conclusion by applying general assumptions, procedures, or principles. 

Example 3: 

Example:

        Each four neighbors, Sean, Maria Sarah and Brian, has different occupation (editor, banker, chef or dentist). From the following clues, determine the occupation of each neighbor.

• Maria gets home from work after the banker but before the dentist. 
• Sarah, who is the last to get home from work, is not the editor. 
• The dentist and Sarah leave for work at the same time. 
• The banker lives next door to Brian.

Solution: 

        From the clue 1. Maria is not the banker or the dentist. In the following chart, write X1 (which stands for “ruled out by clue 1”) in the Banker and the dentist columns of Maria`s row.

        From clue 2, Sarah is not the editor. Write X2 (ruled out by clue 2) in the Editor column of Sarah`s row. We know from clue 1 that the banker is not the last to get home; therefore, Sarah is not the banker. Write X2 in the Banker column of Sarah`s row.

        From clue 3, Sarah is not the dentist. Write X3 for this condition. There are now Xs for three of the four occupation in Sarah`s row; therefore, Sarah must be the chef. Place a √ in that box. Since Sarah is the chef, none of the other three people can bet he chef. Write X3 for this conditions. There are now Xs for three of the four occupations in Maria`s row; therefore, Maria must be the editor. Insert a √ to indicate that Maria is the editor, and write X3 twice to indicate that neither Sean nor Brian is the editor.

  

      From clue 4, Brian is not the Banker. Write X4 for this condition. See the following table. Since there are three Xs in the Banker column, Sean must be the Banker. Place a √ in that box. Thus Sean cannot be the dentist. Write X4 in that box. Since there are 3 Xs in the Dentist column, Brian must be the dentist. Place a √ in that box.

Therefore, Sean is the banker, Maria is the editor, Sarah is the chef, and Brian is the dentist.