Math Problem Statement
Solution
The image you've shared shows a logical circuit involving a NOT gate. The NOT gate inverts the input value, meaning:
- If the input (denoted as ) is true, the output will be false.
- If the input is false, the output will be true.
Looking at the answer options:
-
The output will be true no matter what the value of input B is.
This is incorrect because the output depends on the value of . -
The output will be false no matter what the value of input B is.
This is incorrect for the same reason as above. -
If B is true, then output will be true. If B is false, then output will be false.
This is incorrect because it describes a direct relationship (not inversion). -
If B is true, then output will be false. If B is false, then output will be true.
This is correct because it correctly represents the behavior of the NOT gate.
Therefore, the correct answer is:
"If B is true, then output will be false. If B is false, then output will be true."
Would you like a further breakdown of how logic gates work?
Here are 5 questions that might interest you:
- What is the difference between AND, OR, and NOT gates?
- How can multiple logic gates be combined to form more complex circuits?
- What is the truth table for a NOT gate?
- How do XOR gates work and how are they different from OR gates?
- Can you explain De Morgan's Laws in logic?
Tip: When studying logic gates, practicing with truth tables can help visualize how different inputs affect outputs.
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Math Problem Analysis
Mathematical Concepts
Boolean Algebra
Logic Gates
Formulas
NOT Gate Formula: output = NOT(input)
Truth Table for NOT Gate
Theorems
Inversion Theorem
Basic Boolean Theorems
Suitable Grade Level
Grades 9-12