Home
Class 12
PHYSICS
Prove the following Boolean relations: ...

Prove the following Boolean relations:
`bar(A)+AB+bar(AB)=1`

Text Solution

Verified by Experts

LHS = `bar(A) + AB + bar(AB) = bar(A) + AB + bar(A) + bar(B) = bar(A) + bar(B) + AB`
[`because bar(AB) = bar(A) + bar(B) and bar(A) + bar(A) = bar(A)`]
`=bar(A).1 + bar(B)+AB = bar(A)(1 + B) + bar(B) + AB " "[because 1 + B = 1]`
`bar(A) +bar(A)B + bar(B) +AB = bar(A) + bar(B) + (bar(A)+A)B`
=`bar(A) +bar(B) +1.B = bar(A) + (bar(B)+B) = bar(A) + 1 = 1 = RHS`
Promotional Banner

Topper's Solved these Questions

  • DIGITAL CIRCUITS

    CHHAYA PUBLICATION|Exercise NCERT TEXTBOOK QUESTIONS WITH ANSWER HINT|2 Videos

  • DIGITAL CIRCUITS

    CHHAYA PUBLICATION|Exercise EXERCISE|7 Videos

  • DIGITAL CIRCUITS

    CHHAYA PUBLICATION|Exercise SECTION RELATED QUESTIONS|28 Videos

  • DIFFRACTION AND POLARISATION OF LIGHT

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|27 Videos

  • ELECTRIC ENERGY AND POWER

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|7 Videos

Similar Questions

Explore conceptually related problems

Prove the following boolean relations. bar(bar(A)+AB+bar(AB)) = 0

Prove the following Boolean relations: bar(A)BC+Abar(B)C+ABbar(C)+ABC=AB+BC+CA

Prove the following Boolean relations: ABC+bar(A)BC+bar(B)CD=BC+CD

Prove the following Boolean relations: ABC+bar(A)BC+Abar(B)C+bar(A)bar(B)C+bar(A)Bbar(C)+bar(A)bar(B)bar(C)=bar(A)+C

Prove the following Boolean relations: A+AB+bar(A)B= bar(bar(A)bar(B)

Prove the following Boolean relations: AB+bar(B)C+CA=AB+bar(B)C

Prove the following boolean relations. AB + Abar(B) + bar(A)bar(B) = A + bar(B)

Prove the following Boolean relations: bar(A+bar(B))+bar(bar(A)+bar(B))=B

Prove the following boolean relations : (A + B)(bar(A) + B)bar(B) = 0

Prove the following boolean relations : A(A + bar(A)) + B = A + B

CHHAYA PUBLICATION-DIGITAL CIRCUITS -HIGHER ORDER THINKING SKILL (HOTS) QUESTIONS
  1. Waveforms of two inputs A and B and output Y are shown in Fig. 2.40. F...

    Text Solution

    |

  2. Write the Boolean expression and the truth table for the logic circuit...

    Text Solution

    |

  3. Write the Boolean expression and the truth table for the logic circuit...

    Text Solution

    |

  4. Find the Boolean expression of the given logic circuit in Fig. 2.44. D...

    Text Solution

    |

  5. Two digital signals A and B shown in Fig. 2.46 are used as the two inp...

    Text Solution

    |

  6. Find the Boolean expression of the given logic circuit in Fig. 2.48. D...

    Text Solution

    |

  7. Find the Boolean experssion from the given truth table and draw its si...

    Text Solution

    |

  8. How would you construct an AND gate by using minimum number of OR and ...

    Text Solution

    |

  9. Find the Boolean expression from the given truth table and draw its si...

    Text Solution

    |

  10. How would you construct an OR gate by using minimum number of AND and ...

    Text Solution

    |

  11. Show that the two circuits, shown in Fig. 2.54(a) and Fig. 2.54(b) are...

    Text Solution

    |

  12. Show that the two circuits shown in Fig. 2.55(a) and Fig.2.55(b) are e...

    Text Solution

    |

  13. Two digital signals A and B are represented by two binary numbers 1100...

    Text Solution

    |

  14. Prove the following Boolean relations: bar(A+bar(B))+bar(bar(A)+bar(...

    Text Solution

    |

  15. Prove the following Boolean relations: A+AB+bar(A)B= bar(bar(A)bar(B)

    Text Solution

    |

  16. Prove the following Boolean relations: ABC+bar(A)BC+bar(B)CD=BC+CD

    Text Solution

    |

  17. Prove the following Boolean relations: bar(A)+AB+bar(AB)=1

    Text Solution

    |

  18. Prove the following Boolean relations: AB+bar(B)C+CA=AB+bar(B)C

    Text Solution

    |

  19. Prove the following Boolean relations: bar(A)BC+Abar(B)C+ABbar(C)+ABC...

    Text Solution

    |

  20. Prove the following Boolean relations: ABC+bar(A)BC+Abar(B)C+bar(A)ba...

    Text Solution

    |