Logic (Section 1.1)

Definition: true statement

a sentence (not a question) that is correct all the time

Definition: false statement

a sentence (not a question) that has at least 1 case that isn’t true

Definition: counter-example

an example for a false statement when the statement isn’t correct

Is the following statements true or false? If false, find a counter-example.

All non-negative integers are positive.

false

counter example: 0, not positive or negative

Is the following statements true or false? If false, find a counter-example.

All right triangles have a 30-degree angle.

false

counter example: 90 degree + 45 degree + 45 degree angles

Is the following statements true or false? If false, find a counter-example.

The (positive) root of 9 is 3.

true

Find a counter-example for the statement:

If the sum of 2 integers is even, then both integers must be even.

5 + 5 = 10

For each of the situations below, determine whether it is using inductive or deductive reasoning.

Find the next term for the sequence: 1, 2, 3, 4, 5, ...

inductive reasoning

For each of the situations below, determine whether it is using inductive or deductive reasoning.

All rectangles are polygons with exactly 4 right angles. Figure 1 has 4 right angles and is polygon. Therefore, figure 1 is a rectangle.

deductive reasoning

For each of the situations below, determine whether it is using inductive or deductive reasoning.

Suppose you have 4 siblings. Each of your 4 siblings has bought a lottery ticket. Your friend then concludes that you also must have purchased a lottery ticket.

inductive reasoning

Definition: Inductive Reasoning

The process of reaching a general conclusion by examining specific examples

Definition: Deductive Reasoning

The process of reaching a conclusion by applying general assumptions, principles, or procedures (ie: known facts)

Which type of reasoning uses patterns and examples to make an educated guess of what’s going on in general?

inductive reasoning

Which type of reasoning uses known facts to apply to your specific situation?

deductive reasoning

Use inductive reasoning to predict the most probable next number in each list.

8, 12, 20, 32, 48, 68, ?

92

Use inductive reasoning to predict the most probable next number in the list.

1, 4, 9, 16, 25, 36, 49, 64, ?

81

Use inductive reasoning to predict the most probable next number in the list.

4, 11, −3, 4, −10, −3, −17, −10, −24, ?

-17

Determine whether the argument is an example of inductive reasoning or deductive reasoning.

Emma enjoyed reading the novel Finders Keepers by Stephen King, so she will enjoy reading his next novel.

inductive reasoning

Determine whether the argument is an example of inductive reasoning or deductive reasoning.

Every English setter likes to hunt. Duke is an English setter, so Duke likes to hunt.

deductive reasoning

Determine whether the argument is an example of inductive reasoning or deductive reasoning.

A number is a "neat" number if the sum of the cubes of its digits equals the number. Therefore, 153 is a "neat" number.

deductive reasoning

Find a pair of numbers that provides a counterexample to show that the given statement is false.

If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even counting number.

1 + 5