Show that if F and G are Boolean functions represented by Boolean expressions in n variables and F = G , then F d and G d , where F d and G d are the Boolean functions represented by the duals of the Boolean expressions representing F and G , respectively. [Hint: Use the result of Exercise 29.] *29. Suppose that F is a Boolean function represented by a Boolean expression in the variables x 1 ..., x n . Show that F d ( x 1 , ... , x n ) = F ( x 1 ¯ , ... , x n ¯ ) ¯
Show that if F and G are Boolean functions represented by Boolean expressions in n variables and F = G , then F d and G d , where F d and G d are the Boolean functions represented by the duals of the Boolean expressions representing F and G , respectively. [Hint: Use the result of Exercise 29.] *29. Suppose that F is a Boolean function represented by a Boolean expression in the variables x 1 ..., x n . Show that F d ( x 1 , ... , x n ) = F ( x 1 ¯ , ... , x n ¯ ) ¯
Show that ifFandGare Boolean functions represented by Boolean expressions in n variables andF=G, thenFdandGd, whereFdandGdare the Boolean functions represented by the duals of the Boolean expressions representingFandG, respectively.
[Hint: Use the result of Exercise 29.]
*29. Suppose thatFis a Boolean function represented by a Boolean expression in the variablesx1...,xn. Show that
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use the prime numbers p = 3 and q = 11
Using the public key e = 3, post a phrase about Boolean Functions. Include only letters and spaces in your phrase. Represent the letters A through Z by using the numbers 01 through 26, and represent a space by the number 32. Treat upper case and lower case letters as the same.
How did you calculate your value for d? As a check, the phrase "A CAB" would be represented by "01 32 03 01 02" and would be encrypted as "01 32 27 01 08"
Use a table to express the values for the following Boolean function:
Chapter 12 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Finite Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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