(a.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “If it is raining, then the grass is wet.”
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 “If it is raining, then the grass is wet.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
(b.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “If it is not raining, then the grass is wet.”
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 “If it is not raining, then the grass is wet.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
(c.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “If it is raining, then the grass is not wet.”
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 “If it is raining, then the grass is not wet.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
(d.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “The grass is wet if it is raining.”
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 “The grass is wet if it is raining.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
(e.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “The grass is not wet implies that it is not raining.”
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 “The grass is not wet implies that it is not raining.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
(f.)
The given statement in symbolic form.
It has been determined that the given statement can be written in symbolic form as
Given:
The statement to be written in symbolic form is “The grass is wet if, and only if, it is raining.”
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 “The grass is wet if, and only if, it is raining.”
It is given that
Then, the given statement can be written in symbolic form as
Conclusion:
It has been determined that the given statement can be written in symbolic form as
Chapter B.2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning