Question #181762

Using a Truth table, determine the value of the compound proposition ((𝑝 √ 𝑞) ∧ (ïżąđ‘ √ 𝑟)) → (𝑞 √ 𝑟).


1
Expert's answer
2021-05-02T07:53:51-0400

First, remember the truth tables for basic logical operations :




Before constructing a truth table for the specified expression, we will define a sequence of logical operations. We will denote by numbers from above operations.



((p√(1)q)∧(4)(ÂŹp√(2)r))⟶(5)(q√(3)r)\left(\left(p\lor^{(1)} q\right)\land^{(4)}\left(\neg p\lor^{(2)} r\right)\right)\longrightarrow^{(5)}\left(q\lor^{(3)} r\right)

Now we can construct a truth table for the specified expression.





Q.E.D.


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