Hi, I'm having trouble finding the overall output.
output at A is pq
output at B is ~q+r
output at C is ~p(~q+r)
What is is the overall output? I'm having trouble getting the EXACT answer with parethesis. Please help!! Thanks and God Bless!!
To find the overall output, we need to simplify the expression ~p(~q+r) by applying the rules of Boolean algebra. Let's break it down step by step:
1. According to the expression, the output at C is ~p(~q+r).
2. Note that ~p means the negation of p, and it is outside the parentheses. Following the order of operations, the first step is to distribute the negation ~p to the terms inside the parentheses.
~p(~q+r) will become (~p~q) + (~p~r) after distributing ~p.
3. Next, we need to simplify (~p~q) + (~p~r) using De Morgan's Laws:
De Morgan's Laws state that ~(p+q) is equal to ~p ~q and ~(p*q) is equal to ~p+~q.
Applying De Morgan's Laws to (~p~q) + (~p~r), we get (~pq) + (~pr).
4. Lastly, we need to apply the distributive property. The expression (~pq) + (~pr) can be rewritten as (~pq) + (~pr) = ~(q*r).
Therefore, the overall output is ~(q*r).
If you have any further questions, please let me know!