I have to come up with a logical statement when making a truth table that has these conditions:

The statement is always false if both P and Q are true. Otherwise, the statement is true if Q is true but R is not true.

so far I have ~(P&Q) which makes it false if both P and Q are true. But, I don't know what to add to fulfil the second part.
help!

We want the truth table to look like this:

PQR S
TTT F
TTF F

TFT F
TFF F
FTT F
FTF T
FFT F
FFF F

Looks like it reduces to Q&~(P|R)

To create a logical statement that meets the given conditions, you can use the following steps:

1. Identify the conditions:
- The statement must be false if both P and Q are true.
- The statement must be true if Q is true but R is not true.

2. Translate each condition into logical operators:
- The first condition can be represented as ¬(P ∧ Q), which means "not (P and Q)."
- The second condition can be represented as Q ∧ ¬R, which means "Q and not R."

3. Combine the two conditions using the logical operator "OR" (represented by ∨):
- The final logical statement would be (¬(P ∧ Q)) ∨ (Q ∧ ¬R).
This can be read as "not (P and Q) OR (Q and not R)."

This statement will be false only when both P and Q are true. Otherwise, it will be true if Q is true but R is not true.
Now, you can create the truth table for this logical statement by assigning true or false values to P, Q, and R and evaluating the expression for each combination.