Savvas Learning Co Geometry Student Edition Chapter 2 Reasoning And Proof Exercise 2.2 Logic And Truth Tables
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.
Page 96 Exercise 2 Problem 2
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∧t).
Conjunction (∧) is used to join two sentences using “and”
Disjunction (∨) is used to join two sentences using “or”
Thus we get the compound sentences as s∨(j∧t):
We will go to the beach or we will go out to dinner and movie.
Thus, the compound sentence is s∨(j∧t): We will go to the beach or we will go out to dinner and movie.
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
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.
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”.
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“.
Page 97 Exercise 7 Problem 7
Given: Truth table
To find – Fill the missing values
The complete truth table is :
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
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:
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:
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
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
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
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
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
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
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
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
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
