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Problem 13: (Distributive Laws With Truth Tables)

Let $P$, $Q$, and $R$ be statements or open sentences. Use truth tables to prove each of the following.

  1. Prove that $(P\wedge Q)\vee R$ is equivalent to $(P\vee R)\wedge (Q\vee R)$.
  2. Prove that $(P\vee Q)\wedge R$ is equivalent to $(P\wedge R)\vee (Q\wedge R)$.

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