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Help - Truth Table
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Help - Truth Table











































let p,q,and r represent the following statements: p:3=6=9,q:5*9=40,r:5-7=2
Use the table below each of your assigned problems to write out each step needed to solve the problem along with the calculations necessary to find the answer to your assigned problem.
• The “Calculations” column needs to show each step that you would need to write out if you were showing your work when doing this problem by hand or trying to teach the concept to a friend.
• For each step, you will also have to provide a thorough a description of your thought processes for the calculation in the “Explanations” column.
• The first row (or step) should always be to copy the entire problem into the “Calculations” column or write out the important information. You can use copy and paste.
• Make sure that your final answer is clearly stated.
• You do not have to use all of the rows provided. However, if you need more rows to write out all of the steps you took to complete the problem, add rows.
Week 2

W2.1
Combine the three simple statements below in a compound sentence of the form .

p: this is an orange
q: the monkey is tall
r: I will eat chocolate

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.2
Construct a truth table for .

Calculations Explanations
4 Copy the problem or write out important information.
(Add rows as needed).

W2.3

Let p, q and r represent the following statements:

p: 3 + 6 = 9
q: 5 x 9 = 40
r: 5 – 7 = 2

Determine the truth-value for the statement.

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.4

Construct a truth table for .

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.5
Construct a truth table for .

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

Comments for Help - Truth Table

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Jun 26, 2011
Help - Truth Table
by: Staff

W2.2

Construct a truth table for p∨q → p∧q.


∧: "and"symbol
∨: "or" symbol
~: "negation" (not) symbol

......p....q....p∨q

1....T....T.....T
2....T....F.....T
3....F....T.....T
4....F....F.....F


......p....q....p∧q

1....T....T.....T
2....T....F.....F
3....F....T.....F
4....F....F.....F

...p∨q......p∧q.....p∨q → p∧q

1....T...........T..................T
2....T...........F..................F
3....T...........F..................F
4....F...........F..................T


W2.3

Let p, q and r represent the following statements:

p: 3 + 6 = 9
q: 5 x 9 = 40
r: 5 - 7 = 2

Determine the truth-value for the statement: (p∧~q) →~r

The truthfulness of the statement (p∧~q) →~r is called the truth-value. It is based on classical, or two valued logic (true of false).

The truth-value for the statement (p∧~q) →~r is "TRUE".


If "p" is true and "~q" is true, then "~r" is true.

If 3+6=9 is true and 5 x 9 ≠40 is true, then 5-7≠2 is true.

The truth-value ("logical value" is an equivalent term) of the statement (p∧~q) →~r can be tested using a Truth Table.


All possible combinations of p, q, and r are shown in the following Truth Table. There are 8 possible combinations (2³ = 8):

......p.......q........r

1....T......T........T
2....T......T........F
3....T......F........T
4....T......F........F
5....F......T........T
6....F......T........F
7....F......F........T
8....F......F........F


......p.......~q........~r

1....T........F.........F
2....T........F.........T
3....T........T.........F
4....T........T.........T
5....F........F.........F
6....F........F.........T
7....F........T.........F
8....F........T.........T

......p.......~q........~r........ (p∧~q) →~r

1....T........F.........F...............T
2....T........F.........T...............T
3....T........T.........F...............F
4....T........T.........T...............T
5....F........F.........F...............T
6....F........F.........T...............T
7....F........T.........F...............T
8....F........T.........T...............T

......p.......~q........~r........ (p∧~q) →~r

4....T........T.........T...............T


The truth-value for the statement (p∧~q) →~r is "TRUE".

W2.4

Construct a truth table for q∨~p .

......p....q

1....T....T
2....T....F
3....F....T
4....F....F

.....~p.....q

1....F......T
2....F......F
3....T......T
4....T......F

.....~p......q......q∨~p

1....F........T.........T
2....F........F.........F
3....T........T.........T
4....T........F.........T


Thanks for writing.

Staff
www.solving-math-problems.com

Jun 26, 2011
Help - Truth Table
by: Staff

Part I

The question:

let p,q,and r represent the following statements: p:3=6=9,q:5*9=40,r:5-7=2
Use the table below each of your assigned problems to write out each step needed to solve the problem along with the calculations necessary to find the answer to your assigned problem.
* The "Calculations" column needs to show each step that you would need to write out if you were showing your work when doing this problem by hand or trying to teach the concept to a friend.
* For each step, you will also have to provide a thorough a description of your thought processes for the calculation in the "Explanations" column.
* The first row (or step) should always be to copy the entire problem into the "Calculations" column or write out the important information. You can use copy and paste.
* Make sure that your final answer is clearly stated.
* You do not have to use all of the rows provided. However, if you need more rows to write out all of the steps you took to complete the problem, add rows.


Week 2

W2.1

Combine the three simple statements below in a compound sentence of the form .

p: this is an orange
q: the monkey is tall
r: I will eat chocolate

Calculations Explanations

1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.2
Construct a truth table for p∨q → p∧q.

Calculations Explanations

4 Copy the problem or write out important information.
(Add rows as needed).

W2.3

Let p, q and r represent the following statements:

p: 3 + 6 = 9
q: 5 x 9 = 40
r: 5 - 7 = 2

Determine the truth-value for the statement.

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.4

Construct a truth table for q∨~p.

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

W2.5
Construct a truth table for .

Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).

---------------------------------------------
Part II

The answer:

W2.1

Combine the three simple statements below in a compound sentence of the form .

p: this is an orange
q: the monkey is tall
r: I will eat chocolate

The answer: "If this is an orange and the monkey is not tall, then I will eat chocolate."


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