Logic Mathematics and Logic Gates: gate have same truth table as P ∨ ¬(Q ∧ R)

[Nick S.]

Logic Mathematics and Logic Gates: gate have same truth table as P ∨ ¬(Q ∧ R)

I have soon a test in logic gates, one of the questions is similar to this one:

Find another Logic Gate producing the same Truth Table:
1. P ∨ ¬(Q ∧ R)

Those kind of questions take a lot of time, after a ton of trial and error I got this solution:
R ⇒ (P ∨ ¬Q)

This took a lot of time, by the time it took me to find this solution half of the test time is already over, I wanted to know if someone can help me finding a simple way of finding similar Logic Gates that can produce equal Truth Tables, without trial and error, and if so, at least a way that won't consume a lot of time.

 

[soroban]

I have soon a test in logic gates, one of the questions is similar to this one:

Find another Logic Gate producing the same Truth Table:
1. P ∨ ¬(Q ∧ R)

Those kind of questions take a lot of time, after a ton of trial and error I got this solution:
R ⇒ (P ∨ ¬Q)

Do you know DeMorgan's Rule?

We have: \(\displaystyle \sim (p \vee q) \;=\;\sim p\, \wedge \sim q \)
. . . . or: \(\displaystyle \sim (p \wedge q) \;=\;\sim p\, \vee \sim q\)

How about this equivalence? .\(\displaystyle p \to q\;=\;\sim p \,\vee q\)