Now let us consider the theorems that help in simplifying Boolean functions.

**Idempotency Theorem**The idempotency theorem states that if*P*is a logical or Boolean variable such that*P*can take values ‘0’ or ‘1’ then*P*+*P*=*P*. This can be verified from the truth table given in Table 17.8. The dual of the idempotency theorem states that if*P*is a logical or Boolean variable such that*P*can take values ‘0’ or ‘1’ then*P*.*P*=*P*. This can be verified from the truth table given in Table 17.9.**FIGURE 17.8**The realization of*f*=*PQ*+ using ...

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