Question

Use De Morgan’s laws to find the negation of each of the following statements.

(a) Kewame will take a job in industry or go to graduate school.

(b) Yoshiko knows Java and calculus.

(c) James is young and strong.

(d) Rita will move to Oregon or Washington.

Short answer

Use the De Morgan law for finding the negation of given statements. According to the De Morgan law, the negation of the statement is obtained by replacing “and” with “or” and also adding “not” to both parts of the statement and vice versa.

Step-by-step solution

Definition of De Morgan’s law  

ADe Morgan’s law states that if two inputs are AND'ed and negated, the result is the OR of the respective variables' complements.of these inputs and vice versa.

To find of negation of statements using De Morgan’s law

(a) Kewame will take a job in industry or go to graduate school.

The negation of the above statement is replaces “or” with “and”. Also, add a “not” to both sections of a statement.

The negation of a statement “Kewame will take a job in industry or go to graduate school” is “Kewame will not take a job in industry and not go to graduate school”.

(b) Yoshiko knows Java and calculus.

The negation of the above statement is replaces “and” with “or”. Also, add a “not” to both parts of a statement.

The negation of a statement “Yoshiko knows Java and calculus” is “Yoshiko does not know Java or does not know calculus.”

(c) James is young and strong.

The negation of the above statement is replaces “and” with “or”. Also, add a “not” to both portions of a statement.

The negation of a statement “James is young and strong” is “James is not young or not strong”.

(d) Rita will move to Oregon or Washington.

The negation of the above statement is replaces “or” with “and”. Also, add a “not” to both parts of a statement.

The negation of a statement “Rita will move to Oregon or Washington” is “Rita will not move to Oregon and will not move to Washington”.

Therefore, the statement is negated by using De Morgan’s.