Determine Frequency with simple maths - Permutation, Combination for Digital Logic

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graphene

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Hi I am designing inputs for a 2 input AND gate and i want the possible combinations shown below to be obtained with the 2 signals to be generated. I am unable to determine the frequency of the 2 signls that would match the criteria mentioend below.
Note: Up refers signal going from logic 0 to 1, DOWN refers to signal going to logic from 1 from 0. I need 2 frequencies matching th
 

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