Negation of a logical statement
from class: Math for Non-Math Majors Definition A negation of a logical statement is the opposite of the original statement, often formed by adding 'not.' It changes a true statement to false and vice versa.
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Predict what's on your test 5 Must Know Facts For Your Next Test Negating a universal quantifier (e.g., 'for all') results in an existential quantifier (e.g., 'there exists'), and vice versa. The negation of 'A and B' is 'not A or not B' based on De Morgan's laws. The negation of 'A or B' is 'not A and not B', also based on De Morgan's laws. Negating a conditional statement 'If A then B' results in 'A and not B'. Double negation returns the original statement, i.e., 'not (not A)' is equivalent to 'A'. Review Questions What is the negation of the statement: All students are present? How do you negate the conditional statement: If it rains, I will stay home? Apply De Morgan’s law to negate the following: Either it is raining, or it is snowing.
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