Assignment 14 Query

#$&*

course Mth 151

12/16 8

014. `query 14

********************************************* Question: `q3.3.5 rewrite using if then ' all marines love boot camp '. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Equivalent solution - “If it is a marine, he/she loves boot camp” Not equivalent solution - “If it is boot camp, then all marines will love it” (this statement depicts the original statement on how if it is a marine, then he or she loves boot camp. This is not always true. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent. The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating:2 ********************************************* Question: `q3.3.18 ~p false q false p -> q true YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If ~p is false, then p has to be true because the conditional statement is false. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** Since ~p is false then p is true. Since q is false it follows that p -> q is of the form T -> F, which is false. The conditional is false when, and only when, the antecedent is true and the consequent false. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.36 write in symbols 'If we don't bike, then it does not rain.' YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: p -> ~r confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.48 q true, p and r false, evaluate (-r U p) -> p YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (-r U p) is true and p becomes false since we have one true statement. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** The antecedent (~r U p ) would be true, since ~r true and p false. The consequent p would be false. Since the antecedent is true and the consequent false, the conditional is false. ** MORE DETAILED SOLUTION r is said to be false, so ~r is true p is said to be false Therefore the disjunction (~r U p) would be a disjunction of a true and a false statement. A disjunction is true if at least one of the statements is true, so (~r U p) is true. The conditional (~r U p) -> p therefore consists of an antecedent which is true, and a consequent which is false. By the rules for a conditional, the statement is therefore false. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: p, q ,(p^q), (pUq), (p^q)->(pUq) 1st row - TTTTT 2nd row - TFFTT 3rd row - FTFTT 4th row- FFFFT confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq) Row 1 would read T T T T T Row 2 would read T F F T T Row 3 would read F T F T T Row 4 would read F F F F T The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q). The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating:2 ********************************************* Question: `qQuery 3.3.74 (formerly 3.3.72). This wasn't assigned but it is similar to assigned questions and should be answered: What is the negation of the statement 'if loving you is wrong then I don't want to be right' ? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: “Loving you is wrong and I want to be right” (opposite of the original statement) confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: `a** The negation has to have the exact opposite truth values of the original statement. It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws. Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q. So the negation would ge 'loving you is wrong AND I want to be right. COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right. INSTRUCTOR COMMENT: The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):

Assignment 14 Query

#$&*

course Mth 151

12/16 8

014. `query 14

*********************************************

Question: `q3.3.5 rewrite using if then ' all marines love boot camp '.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Equivalent solution - “If it is a marine, he/she loves boot camp”

Not equivalent solution - “If it is boot camp, then all marines will love it” (this statement depicts the original statement on how if it is a marine, then he or she loves boot camp. This is not always true.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent.

The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:2

*********************************************

Question: `q3.3.18 ~p false q false p -> q true

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

If ~p is false, then p has to be true because the conditional statement is false.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** Since ~p is false then p is true.

Since q is false it follows that p -> q is of the form T -> F, which is false.

The conditional is false when, and only when, the antecedent is true and the consequent false. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `qQuery 3.3.36 write in symbols 'If we don't bike, then it does not rain.'

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p -> ~r

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `qQuery 3.3.48 q true, p and r false, evaluate (-r U p) -> p

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(-r U p) is true and p becomes false since we have one true statement.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** The antecedent (~r U p ) would be true, since ~r true and p false.

The consequent p would be false.

Since the antecedent is true and the consequent false, the conditional is false. **

MORE DETAILED SOLUTION

r is said to be false, so ~r is true

p is said to be false

Therefore the disjunction (~r U p) would be a disjunction of a true and a false statement.

A disjunction is true if at least one of the statements is true, so (~r U p) is true.

The conditional (~r U p) -> p therefore consists of an antecedent which is true, and a consequent which is false.

By the rules for a conditional, the statement is therefore false.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:3

*********************************************

Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q)

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

p, q ,(p^q), (pUq), (p^q)->(pUq)

1st row - TTTTT

2nd row - TFFTT

3rd row - FTFTT

4th row- FFFFT

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq)

Row 1 would read T T T T T

Row 2 would read T F F T T

Row 3 would read F T F T T

Row 4 would read F F F F T

The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q).

The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:2

*********************************************

Question: `qQuery 3.3.74 (formerly 3.3.72). This wasn't assigned but it is similar to assigned questions and should be answered: What is the negation of the statement 'if loving you is wrong then I don't want to be right' ?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

“Loving you is wrong and I want to be right” (opposite of the original statement)

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

`a** The negation has to have the exact opposite truth values of the original statement.

It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws.

Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q.

So the negation would ge 'loving you is wrong AND I want to be right.

COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right.

INSTRUCTOR COMMENT:

The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):