Question

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

(a) Jan is rich and happy.

(b) Carlos will bicycle or run tomorrow.

(c) Mei walks or takes the bus to the class.

(d) Ibrahim is smart and hard working.

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  

A De 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) Jan is rich and happy.

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

The negation of a statement “Jan is rich and happy” is “Jan is not rich or not happy”.

(b) Carlos will bicycle or run tomorrow.

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 “Carlos will bicycle or run tomorrow” is “Carlos will not bicycle or not run tomorrow.”

(c) Mei walks or takes the bus to the class.

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

The negation of a statement “Mei walks or takes the bus to the class” is “Mei does not walk or does not take the bus to the class”.

(d) Ibrahim is smart and hard working.

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 “Ibrahim is smart and hard working” is “Ibrahim is not a smart or not hard working”.

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