Savvas Learning Co Geometry Student Edition Chapter 2 Reasoning And Proof Exercise 2.2 Logic And Truth Tables

Savvas Learning Co Geometry Student Edition Chapter 2 Reasoning And Proof Exercise 2.2 Logic And Truth Tables

Savvas Learning Co Geometry Student Edition Chapter 2 Exercise 2.2 Logic And Truth Tables Solutions Page 96  Exercise 1  Problem 1

Given:

s: We will go to the beach.

j: We will go out to dinner.

t: We will go to the movies.

To find – Construct the compound statements of s∨j

Disjunction is denoted as ∨

For disjunction we use the word “or” to join two sentences.

Thus, we get s∨j We will go to beach or we will go out to dinner.

Thus, the compound sentence is s∨j: We will go to beach or we will go out to dinner.

Read and Learn More Savvas Learning Co Geometry Student Edition Solutions

Exercise 2.2 Logic And Truth Tables Savvas Geometry Answers Page 96  Exercise 2  Problem 2

Given:

Thus, the compound sentence is s∨(j∧t): We will go to the beach or we will go out to dinner and movie.

Exercise 2.2 Logic And Truth Tables Savvas Geometry Answers Page 96  Exercise 3  Problem 3

Given: Write three of your own statements.

To find –  Construct compound sentences.

Let

s: I will drink coffee

j: I will drink tea

t: I will eat breakfast

Conjunction (∧) is used to join two sentences using “and”

Disjunction (∨)is used to join two sentences using “or”

1. s∧j  = I will drink coffee and I will drink tea.

2. s∨j = I will drink coffee or I will drink tea.

3. s∨(j∧t) =  I will drink coffee or I will drink tea and eat breakfast

4. (s∨j)∧t = I will drink coffee or tea and eat breakfast

Thus, we get I will drink coffee and I will drink tea.I will drink coffee and I will drink tea.I will drink coffee or I will drink tea and eat breakfast I will drink coffee or tea and eat breakfast

Logic And Truth Tables Solutions Chapter 2 Exercise 2.2 Savvas Geometry Page 96  Exercise 4  Problem 4

Given: x∧y

To find –  Use the statements to determine the truth value of the compound statement.

Considering the statement  x∧y 

Emperor penguins are black and white and Polar bears are a threatened species.

Conjunction x∧y is true only if both the statement is true .

Since given both the statements are true therefore x∧y is true compound sentence.

Thus ,compound sentence x∧y is true.

Logic And Truth Tables Solutions Chapter 2 Exercise 2.2 Savvas Geometry Page 96  Exercise 5  Problem 5

Given: x∨y

To find – Use the statements to determine the truth value of the compound statement.

Considering the statements we get

x∨y: Emperor penguins are black and white and Polar bears are a threatened species.

Disjunction x∨y is false only if both the statements are false.

Since, given both the statement is true therefore the truth value of the compound sentence x∨y is “true”.

Thus, the truth value of the compound sentence x∨y is “true”.

Chapter 2 Exercise 2.2 Logic And Truth Tables Savvas Learning Co Geometry Explanation Page 96  Exercise 6  Problem 6

Given: x∨z

To find – Use the statements to determine the truth value of the compound statement.

Considering the statements

We get x∨z :  Emperor penguins are black and white or Penguins wear tuxedos.

Disjunction of two statement is false only if both the statement is false.

Since, both the given statement is true , therefore the truth value of compound the statement x∨z is “true”

Thus, therefore the truth value of compound the statement x∨z is “true“.

Solutions For Logic And Truth Tables Exercise 2.2 In Savvas Geometry Chapter 2 Student Edition Page 97  Exercise 7  Problem 7

Given: Truth table

To find – Fill the missing values

The complete truth table is :

Solutions For Logic And Truth Tables Exercise 2.2 In Savvas Geometry Chapter 2 Student Edition Page 97  Exercise 8  Problem 8

Given: Truth table of a pattern.

To find –  Fill the missing values.

The truth table

Conjunction (∧) of two statement is true only if both the statements are true

Disjunction (∨) of two statement is false only if both the statements are false

Thus, the complete truth table is

Exercise 2.2 Logic And Truth Tables Savvas Learning Co Geometry Detailed Answers Page 97  Exercise 9  Problem 9

Given: Truth table of a pattern.

To find –  Fill the missing values.

The truth table

Conjunction(∧)of two statement is true only if both the statements are true.

Disjunction (∨)of two statement is false only if both the statements are false.

The complete truth table is:

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 10  Problem 10

Given: Truth table of a pattern.

To find – Fill the missing values.

The true table:

Conjunction (∧)of two statement is true only if both the statements are true.

Disjunction (∨)of two statement is false only if both the statements are false.

The complete truth table is:

Geometry Chapter 2 Logic And Truth Tables Savvas Learning Co Explanation Guide Page 97  Exercise  11  Problem 11

 Given That: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s, j, and j and builds to (s ∧ j) ∨ ∼t.

To find –  To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks……

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by using the functions of symbols ~, ∧, ∨. as

~T = F

⇒ T∧F = F

⇒ T∨F = T

⇒ T∧T = T

⇒ F∧F = F

Now the table is filled by using these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is

For the given table

Geometry Chapter 2 Logic And Truth Tables Savvas Learning Co Explanation Guide Page 97  Exercise 12  Problem 12

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s, j, and j and builds to (s∧j)∨∼t.

To find – To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks ……….

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~T = F

⇒ T ∧F = F

⇒ T∨ F = F

⇒ T∧T = T

⇒ F∧F = F

Now the table is fill by use these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is 

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 13  Problem 13

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s,j, and t builds to (s∧j)∨∼t

.

To find – To find the possible truth values of a complex statement such as(s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks…….

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 14  Problem 14

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement.

The table below starts with columns for s,j, and t builds to (s∧j)∨∼t

To find –  To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks ………

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 15  Problem 15

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s,j, and t builds to (s∧j)∨∼t

To find – To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks ……….

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by using the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is filled by using these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 16  Problem 16

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s,j and t builds to (s∧j)∨∼t

To find – To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks ………….

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 17  Problem 17

Given that: You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s, j and t builds to (s∧j)∨∼t

To find – To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks ………..

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The possible truth values of a complex statement such as (s∧j)∨∼t is 

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 18  Problem 18

Given that:  You can make a truth table like the one below.

You start with columns for the single statements and add columns to the right.

Each column builds toward the final statement. The table below starts with columns for s, j and t builds to (s∧j)∨∼t

To find – To find the possible truth values of a complex statement such as (s∧j)∨∼t.

Copy the table and work with a partner to fill in the blanks …………..

The symbols ~, ∧ ,∨ are not, and, or.

The truth table can be filled by use the functions of symbols ~, ∧, ∨. as

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The possible truth values of acomple statement such as (s∧j)∨∼t is

For the given table

Savvas Learning Co Geometry Student Edition Chapter 2 Page 97  Exercise 19  Problem 19

Given that: (∼p∨q)∧∼r

To find – Make truth table for statement. (∼p∨q)∧∼r

The symbols ~, ∧ ,∨ are not, and, or.

The truth table for the statement is (∼p∨q)∧∼r

~ T = F

⇒ T ∧ F = T

⇒ T ∨ F = T

⇒ T ∧ T = T

⇒ F ∧ F = F

Now the table is fill by use these above results

The truth table for the statement (∼p∨q)∧∼r is