How Does De Morgan's Law Apply to Probability Logic?

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SUMMARY

De Morgan's Law is applied in probability logic to derive the formula for the probability of the union of two events. Specifically, if τ(¬p) = 1 - τ(p) and τ(p∧q) = τ(p)∙τ(q), then it can be shown that τ(p∨q) = τ(p) + τ(q) - τ(p)∙τ(q). This relationship highlights the interdependence of events in probability theory and is essential for understanding how to calculate probabilities of combined events.

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If τ(¬p)=1-τ(p) and τ(p∧q)=τ(p)∙τ(q) show that:
τ(p∨q)=τ(p)+τ(q)-τ(p)∙τ(q)
 
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skaeno said:
If τ(¬p)=1-τ(p) and τ(p∧q)=τ(p)∙τ(q) show that:
τ(p∨q)=τ(p)+τ(q)-τ(p)∙τ(q)

Hi skaeno, welcome to MHB! :)

Perhaps you might consider that p∨q=¬(¬p∧¬q)?
 

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