Chapter B.1, Problem 6E

Solution

(a.)

The given statement in symbolic form.

It has been determined that the given statement can be written in symbolic form as $q\wedge r$ .

Given:

  $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

The statement to be written in symbolic form is “This course is easy and lazy students do not study.”

Concept used:

A compound statement can be written in symbolic form, by denoting each simple statement by a variable and using logical symbols.

Calculation:

The given statement is “This course is easy and lazy students do not study.”

It is given that $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

Then, the given statement can be written in symbolic form as $q\wedge r$ .

Conclusion:

It has been determined that the given statement can be written in symbolic form as $q\wedge r$ .

(b.)

The given statement in symbolic form.

It has been determined that the given statement can be written in symbolic form as $r\vee \sim q$ .

Given:

  $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

The statement to be written in symbolic form is “Lazy students do not study or this course is not easy.”

Concept used:

A compound statement can be written in symbolic form, by denoting each simple statement by a variable and using logical symbols.

Calculation:

The given statement is “Lazy students do not study or this course is not easy.”

It is given that $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

Then, the given statement can be written in symbolic form as $r\vee \sim q$ .

Conclusion:

It has been determined that the given statement can be written in symbolic form as $r\vee \sim q$ .

(c.)

The given statement in symbolic form.

It has been determined that the given statement can be written in symbolic form as $\sim \left(q\wedge r\right)$ .

Given:

  $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

The statement to be written in symbolic form is “It is false that both this course is easy and lazy students do not study.”

Concept used:

A compound statement can be written in symbolic form, by denoting each simple statement by a variable and using logical symbols.

Calculation:

The given statement is “It is false that both this course is easy and lazy students do not study.”

It is given that $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

Then, the given statement can be written in symbolic form as $\sim \left(q\wedge r\right)$ .

Conclusion:

It has been determined that the given statement can be written in symbolic form as $\sim \left(q\wedge r\right)$ .

(d.)

The given statement in symbolic form.

It has been determined that the given statement can be written in symbolic form as $\sim q$ .

Given:

  $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

The statement to be written in symbolic form is “This course is not easy.”

Concept used:

A compound statement can be written in symbolic form, by denoting each simple statement by a variable and using logical symbols.

Calculation:

The given statement is “This course is not easy.”

It is given that $q$ stands for “This course is easy” and $r$ stands for “Lazy students do not study”.

Then, the given statement can be written in symbolic form as $\sim q$ .

Conclusion:

It has been determined that the given statement can be written in symbolic form as $\sim q$ .