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From the given two function P ⊃ ¬) ∨ ¬R & P ∧ ∨ ¬ ⊃ (¬P~) , Write reduced truth tables, then analytical expressions, normal forms (IDNF and IKNF), numerical forms, represented by Karnaut diagrams

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Final answer:

To write reduced truth tables for the given functions, simplify the functions using logical operations and construct Karnaut diagrams.

Step-by-step explanation:

To write reduced truth tables for the given functions, we will evaluate the functions for all possible combinations of truth values for the variables P, Q, and R. We will then simplify the functions using logical operations. Similarly, we can find analytical expressions, normal forms (IDNF and IKNF), and numerical forms. The Karnaut diagrams can be constructed based on the truth tables.

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