Evaluate
Q1: What is the next item in this pattern?
1, 10, 18, 25...
A) 31
Why? Because 10-1=9, 18-10=8, 25-18=7, so ?-25=6. 25+6=31, so 31 is your answer.
Q2: Determine if the following conjecture is valid by the Law of Detachment
Given: If Boyd finishes his homework he can go to the movies. Boyd is at the movies eating popcorn and sour patch kids.
Conjecture: Boyd finished his homework
A) True
Why? Because Boyd has to finish his homework to go to the movies. Boyd is at the movies, so that implies that he finished his homework.
Q3: Is this true by the Law of Syllogism?
Given: If a figure is a square, then the figure is a rectangle. If a figure is a square then it is a parallelogram
Conjecture: If the figure is a parallelogram then it is a rectangle.
B) False
Why? Because for the statement to be true according to the Law of Syllogism, if p → q and q → r are true statements, then p → r has to be a true statement. In this example p → q and p → r are true statements, but q → r is not true, because statement 1 and statement 2 have only the smallest category in common, so the conjecture is false.
Q4: Is the following solved by using inductive or deductive reasoning?
Given: Jorge is going to the Chinese restaurant as soon as he is done with practice. Jorge is now at the Chinese restaurant and disco dance instruction studio
Conclusion: Jorge is done with practice.
B) Deductive
Why? Because Deductive reasoning is based off of facts and is using logic to draw conclusions from statements. Inductive reasoning is using patterns. The above example is facts and logic, so it is Deductive reasoning.
Q5: What are the next two items in this pattern?
>, >^, >^>
A) >^>^, >^>^>
Why? Because in this pattern, every time a new shape is added, it is either > or ^. The shapes change every one shape, so A is the right answer.