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Match the rule name to the rule expression. Only one rule applies to an expressi

ID: 3734102 • Letter: M

Question

 Match the rule name to the rule expression. Only one rule applies to an
 expression. Not all rules may be expressed, and more than one expression may be an example of a rule. Some statements may be incorrect. If so, Use invalid choice.
 A. Identity       B. Null      C. Idempotent     D. Inverse (Complement)
 E. Distribution   F. DeMorgan  G. Cancellation    H. Invalid.
 ____ A*C*D+(B+1)*C*D = A*C*D+1*B*C*D       ____ (A+!A)(B+C) = 1*(B+C)
 ____ A+B+!!(C+D) = A+B+(C+D)               ____ (A+B)*(A+B) = A+B
 ____ A*C*D+B*C*D+C*D = A*C*D+B*C*D+1*C*D   ____ A+B*C=(A+B)*(A+C)
 ____ A*(!B+!C) = A*!B+A*!C                 ____ 0+(B+C) = A+(B+C)+!A

Explanation / Answer

Answer is as follows :

The statement is INVALID(h) becaue we can't make (B+1) * C * D to 1 * B * C * D.

b)  A+B+!!(C+D) = A+B+(C+D)

It uses the double negation law two times to get (C+D) from !!(C+D) (not mentioned in options)

c) A*C*D+B*C*D+C*D = A*C*D+B*C*D+1*C*D

It uses identity law(A) on C*D i.e. equal to 1*C*D.

d) A*(!B+!C) = A*!B+A*!C

It uses distributive law (E) on A*(!B+!C).

e) (A+!A)(B+C) = 1*(B+C)

It uses complement law(d) i.e. A + !A = 1

f) (A+B)*(A+B) = A+B

It uses idepotent law(c) where A + A = A

g) A+B*C=(A+B)*(A+C)

It uses distributive law(e) where A + (B * C) = (A + B)* (A + C)

h) 0+(B+C) = A+(B+C)+!A

The statement is INVALID(h) because A + !A = 1 not 0

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