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06 - Distribution

 1. The distributive/distribution law can also be stated like this: a × (b + c) = a × b + b × a

  False

  True

 2. The Boolean distributivity law is similar to distributivity in normal mathematics and has to do with expanding or simplifying ___________

  full stops

  AND gates

  brackets

  NOT gates

 3. In practice, distribution is often carried out when either an 'AND' or an 'OR' is outside the brackets and the other is inside.

  TRUE

  FALSE

 4. You can think of the distributive law as a law which deals with either 'multiplying out' or factoring. E.g in Maths: x(y+z) could give you:

  xyz

  xz+y

  xy+xz

  xy

 5. Complete the following equation: e AND (f OR g) = (e AND f) OR (e AND g) and e OR (f AND g) = (e OR f) AND _________

  eg+eg

  (eg)

  (e OR g)

  (e AND g)

 6. The distributive law would allow us to arrive at what output, from this expression: (x+y).(x+z)=

  x.x+y

  xyz

  x+(yz)

  xxyy

 7. Using the distributive law, "simplify" the following expression: (A + B)(A + C)

  A.1 + B.C

  A.1 + B.C + C

  A+B+C

  A.A + A.C + A.B + B.C

 8. Using the distributive law it is also possible to simplify (A + B).(A + C) to A(1 + B) + B.C

  TRUE

  FALSE

 9. The expression (A + B)(A + C) can be simplified to ____________using the distributive law.

  A(B.C)

  A + (B.C)

  A.B+C

  ABC

 10. Using the distributive law: X + Y Z = (X + Y) + (X. Z)

  FALSE

  TRUE

 11. Using the distributive law: X. (Y + Z) = X Y + Z

  TRUE

  FALSE

 12. Using the distributive law: X. (Y + Z) = X Y + X Z

  TRUE

  FALSE

 13. Read the excerpt on removing factors below and fill in the blanks for the boolean equivalent
Using the distributive law, you can also remove factors 
(common variables), like in normal algebra. 

For example: if you had (3 * 4) + (3 * 2), this could be 
factorised into 3(4 + 2). 

Note that both answers give 18. 

The Boolean equivalent of this is:

______________________________________?

  (A AND B) OR (A AND C) ? A OR B OR C

  (A AND B) OR (A AND C) ? A AND (B OR C)

  (A AND B) OR (A AND C) ? ABC

  (A AND B) OR (A AND C) ? A AND B

 14. A(B + C) =

  A.B + A.C

  A.B. A.C

  A+.B + A+C

  A.BC

 15. A + (B.C) =

  (A + B).(A + C)

  (A. B).(A.C)

  (A. B)+(A.C)

  (AB+AC)