Worksheet Answers: Boolean Algebra

 

  1.  
    A    		  
    B    		  
    A · B    		  
    A + A · B
    0 0 0 0
    0 1 0 0
    1 0 0 1
    1 1 1 1

    2.  

  2.  
    A    		  
    B    		  
    A    		  
    A · B    		  
    A + A · B
    0 0 1 0 0
    0 1 1 1 1
    1 0 0 0 1
    1 1 0 0 1

    3.  

  3.  
    A    		  
    B    		  
    C    		  
    A · B · C    		  
    A · B · C    		  
    A · B · C + A · B · C
    0 0 0 0 1 1
    00101 1
    0 1 0 0 1 1
    01101 1
    1 0 0 0 1 1
    1 0 1 0 1 1
    1 1 0 0 1 1
    1 1 1 1 0 1

    4.  

  4.  
    0    		  
    P    		  
    0 · P
    0 0 0
    0 1 0

    The values for 0 and 0 · P match in every row, thus the identity is true.

  5.  
    P    		  
    P    		  
    P + P
    0 0 0
    1 1 1

    The values for P and P + P match in every row, thus the identity is true.

  6.  
    P    		  
    Q    		  
    P·Q    		  
    P·Q    		  
    P    		  
    Q    		  
    P + Q
    0 0 0 1 1 1 1
    0 1 0 1 1 0 1
    1 0 0 1 0 1 1
    1 1 1 0 0 0 0

    The values for P·Q and P + Q match in every row, thus the identity is true.

  7.  
    P    		  
    Q    		  
    R    		  
    Q · R    		  
    P · (Q · R)    		  
    P · Q    		  
    (P · Q) · R
    0 0 0 0 0 0 0
    0010000
    0 1 0 0 0 0 0
    0111000
    1 0 0 0 0 0 0
    1010000
    1 1 0 0 0 1 0
    1 1 1 1 1 1 1

    The values for P · (Q · R) and (P · Q) · R match in every row, thus the identity is true.

  8. X Y Z X Y Z XYZ X + Y + XYZ X + Y + Z
    0 0 0 1 1 1 0 1 1
    0 0 1 1 1 0 0 1 1
    0 1 0 1 0 1 0 1 1
    0 1 1 1 0 0 0 1 1
    1 0 0 0 1 1 0 1 1
    1 0 1 0 1 0 0 1 1
    1 1 0 0 0 1 1 1 1
    1 1 1 0 0 0 0 0 0

    The values for X + Y + XYZ and X + Y + Z match in every row, thus the identity is true.

  9. X

  10. S · T + V · W

  11. F

  12. A · B · C · D

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