Chapter B.1, Problem 13E

Solution

(a.)

To Restate: The given statement in a logically equivalent form.

It has been determined that the given statement restated in a logically equivalent form is:

“It is true that either today is not Wednesday or the month is not June.”

Given:

It is not true that both today is Wednesday and the month is June.

Concept used:

Logically equivalent statements are statements with identical truth table values.

Calculation:

The given statement is “It is not true that both today is Wednesday and the month is June.”

Restating the given statement in a logically equivalent form, it follows that:

“It is true that either today is not Wednesday or the month is not June.”

Conclusion:

It has been determined that the given statement restated in a logically equivalent form is:

“It is true that either today is not Wednesday or the month is not June.”

(b.)

To Restate: The given statement in a logically equivalent form.

It has been determined that the given statement restated in a logically equivalent form is:

“It is true that yesterday I either did not eat breakfast or did not watch television.”

Given:

It is not true that yesterday I both ate breakfast and watched television.

Concept used:

Logically equivalent statements are statements with identical truth table values.

Calculation:

The given statement is “It is not true that yesterday I both ate breakfast and watched television.”

Restating the given statement in a logically equivalent form, it follows that:

“It is true that yesterday I either did not eat breakfast or did not watch television.”

Conclusion:

It has been determined that the given statement restated in a logically equivalent form is:

“It is true that yesterday I either did not eat breakfast or did not watch television.”

(c.)

To Restate: The given statement in a logically equivalent form.

It has been determined that the given statement restated in a logically equivalent form is:

“It is not true that it is both raining and is July.”

Given:

It is not raining or it is not July.

Concept used:

Logically equivalent statements are statements with identical truth table values.

Calculation:

The given statement is “It is not raining or it is not July.”

Restating the given statement in a logically equivalent form, it follows that:

“It is not true that it is both raining and is July.”

Conclusion:

It has been determined that the given statement restated in a logically equivalent form is:

“It is not true that it is both raining and is July.”