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06 - Distribution

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

  True

  False

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

  AND gates

  brackets

  NOT gates

  full stops

 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:

  xy

  xz+y

  xy+xz

  xyz

 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 _________

  (e OR g)

  (eg)

  eg+eg

  (e AND g)

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

  xyz

  x.x+y

  xxyy

  x+(yz)

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

  A+B+C

  A.1 + B.C + C

  A.A + A.C + A.B + B.C

  A.1 + B.C

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

  FALSE

  TRUE

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

  ABC

  A.B+C

  A(B.C)

  A + (B.C)

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

  TRUE

  FALSE

 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

  FALSE

  TRUE

 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) ? ABC

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

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

  (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)