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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Finite Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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