text: # Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-min terms asf1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
  
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  ## Options:
  
  1. ∑ (7, 8, 11)
  
  2. ∑ (2, 7, 8, 11, 14)
  
  3. ∑ (2, 14)
  
  4. ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)
  
  ### Correct Answer: Option 1 (Solution Below)
  
  This question was previously asked in
  
  GATE CS 2019 Official Paper
  
  ## Solution:
  
  Let X = f1.f2
  
  = (0, 2, 5, 8, 14).(2, 3, 6, 8, 14, 15)
  
  = (2, 8, 14)
  
  X ⊕ f3
  
  = (2, 8, 14) ⊕ (2, 7, 11, 14)
  
  = (2, 8, 14).(2, 7, 11, 14)’ + (2, 8, 14)’.(2, 7, 11, 14)
  
  = (2, 8, 14).(0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15) + (0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15).(2, 7, 11, 14)
  
  = (8) + (7, 11)
  
  =(7, 8, 11)
  
  (f1.f2) ⊕ f3 = ∑ (7, 8, 11)
explanation: The document describes a problem involving three 4-variable functions expressed in sum-of-min terms. It asks for the output function of a circuit with one AND gate and one XOR gate. The document also provides options for the correct answer and includes a detailed solution that explains the steps to derive the correct answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-min terms asf1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
  
  Free Practice With Testbook Mock Tests
  
  ## Options:
  
  1. ∑ (7, 8, 11)
  
  2. ∑ (2, 7, 8, 11, 14)
  
  3. ∑ (2, 14)
  
  4. ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)
  
  ### Correct Answer: Option 1 (Solution Below)
  
  This question was previously asked in
  
  GATE CS 2019 Official Paper
  
  ## Solution:
  
  Let X = f1.f2
  
  = (0, 2, 5, 8, 14).(2, 3, 6, 8, 14, 15)
  
  = (2, 8, 14)
  
  X ⊕ f3
  
  = (2, 8, 14) ⊕ (2, 7, 11, 14)
  
  = (2, 8, 14).(2, 7, 11, 14)’ + (2, 8, 14)’.(2, 7, 11, 14)
  
  = (2, 8, 14).(0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15) + (0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15).(2, 7, 11, 14)
  
  = (8) + (7, 11)
  
  =(7, 8, 11)
  
  (f1.f2) ⊕ f3 = ∑ (7, 8, 11)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document describes a problem involving three 4-variable functions expressed in sum-of-min terms. It asks for the output function of a circuit with one AND gate and one XOR gate. The document also provides options for the correct answer and includes a detailed solution that explains the steps to derive the correct answer.
  
  Label: question-and-answer