Mathematics: Use logical cquivalences or a truth table to show that (pvq) r to (p r) a (q r)

Use logical cquivalences or a truth table to

Ответ:

impura12713

05.01.2022

The statement $(P\lor Q)\rightarrow R$ is logically equivalent to the statement $(P\rightarrow R) \land (Q\rightarrow R)$

Step-by-step explanation:

We have the following statement $(P\lor Q)\rightarrow R$ and we need to prove that is logically equivalent to this statement $(P\rightarrow R) \land (Q\rightarrow R)$ .

To prove the logical equivalence of the statements we are going to use the table of logical equivalences as follows:

$(P\lor Q)\rightarrow R \equiv \lnot(P\lor Q)\lor R$ by the logical equivalence involving conditional statement.

$\equiv (\lnot P \land \lnot Q)\lor R$ by de Morgan’s laws.

$\equiv (\lnot P\lor R)\land(\lnot Q \lor R)$ by distributive laws.

$\equiv (P\rightarrow R) \land (Q\rightarrow R)$ by the logical equivalence involving conditional statement.

Use logical cquivalences or a truth table to show that (pvq) r to (p r) a (q r)

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Ответ:

amastriano6192

06.04.2022

Mathematics

28561

Step-by-step explanation:

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Use logical cquivalences or a truth table to show that (pvq) r to (p r) a (q r)

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