Math Problem Statement
Negate this expression: NOT(A) AND B
Solution
To negate the expression NOT(A) AND B, we apply De Morgan's Law, which states:
- The negation of a conjunction (AND) is the disjunction (OR) of the negated components.
- The negation of a disjunction (OR) is the conjunction (AND) of the negated components.
The given expression is NOT(A) AND B.
Negating it:
- The negation of the entire expression will be NOT(NOT(A) AND B).
- By De Morgan's Law, this becomes NOT(NOT(A)) OR NOT(B).
- NOT(NOT(A)) simplifies to A.
Thus, the negated expression is:
A OR NOT(B).
Would you like more details or have any questions?
Here are 5 related questions to explore further:
- How does De Morgan's Law work in logic?
- What is the negation of an OR expression?
- How would you simplify NOT(A OR B)?
- What is the truth table for NOT(A) AND B and its negation?
- How can Boolean algebra be used to simplify logical expressions?
Tip: De Morgan's laws are crucial in logic and set theory, and they help simplify complex negations in both fields.
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Math Problem Analysis
Mathematical Concepts
Boolean Algebra
Logic
De Morgan's Law
Formulas
De Morgan's Law: NOT(A AND B) = NOT(A) OR NOT(B)
Theorems
De Morgan's Theorems
Suitable Grade Level
Grades 10-12