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Homework Statement
[(p->r) ^ (q->r)] -> (p ^ q) -> r
Homework Equations
anything but a truth table! laws such as (p->q)= ~(p^~q) or (p->q)=(~q->~p) might help
Simplifying a logical equivalence statement means to reduce it to its most basic form or expression using the properties and laws of logic.
Simplifying a logical equivalence statement allows for easier analysis and understanding of the statement. It also helps to identify any errors or inconsistencies in the statement.
To simplify a logical equivalence statement without a truth table, you can use the properties and laws of logic such as the distributive law, commutative law, and De Morgan's laws. You can also use logical equivalences and identity laws to simplify the statement.
Yes, a logical equivalence statement can have multiple simplifications. This is because there are often multiple ways to apply the properties and laws of logic to simplify a statement.
One common mistake to avoid is overlooking any negations in the statement. It is important to apply De Morgan's laws to correctly simplify the statement. Another mistake is not using parentheses correctly, which can change the meaning of the statement.