Question

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

Answer 1

De Morgan's laws help negate statements by flipping conjunctions to disjunctions and vice versa. For example, the negation of 'Kwame will take a job in industry or go to graduate school' is 'Kwame will not take a job in industry and will not go to graduate school.'

Step-by-step explanation:

To negate a statement using De Morgan's laws, we apply the principle that the negation of a conjunction (and) is the disjunction (or) of the negations, and the negation of a disjunction (or) is the conjunction (and) of the negations. Applying this to the given statements:

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An example of a statement and its negation is 'The cat is on the mat' and the negation 'The cat is not on the mat.'

Regarding the law of noncontradiction, it logically implies the law of the excluded middle because if something cannot both be and not be (noncontradiction), then it must either be or not be (excluded middle), with no third option.

Counterexample is an example that contradicts a statement or proposition. For instance, if a conditional claims all swans are white, a single black swan serves as a counterexample.

Answer 2

a) Kwame will not take a job in industry and not go to graduate school.

b) Yoshiko does not know Java or calculus

c) James is not young nor strong

d) Rita will not move to Oregon and Washington

Step-by-step explanation:

Negation of and is or

Negation of or is and

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

Kwame will not take a job in industry and not go to graduate school.

b) Yoshiko knows Java and calculus

Yoshiko does not know Java or calculus

c) James is young and strong

James is not young nor strong

d) Rita will move to Oregon or Washington

Rita will not move to Oregon and Washington