# How to conclude truth value of elements from true propositions

suppose that these propositions are true $$\qquad \neg (\neg d \lor a) \ , \quad (\neg a \land c) \lor d \ , \quad a \lor \neg b \ , \quad c \rightarrow b$$

What are the value(s) of Truth of a, b, c and d?

I got an exercice like that and I'm not sure if my method is correct mainly because the question states that an element could have more than one value of truth

Answer... $$a$$: False, $$b$$: False, $$c$$: False, $$d$$: True

We have: $$\neg (\neg d \lor a) \Leftrightarrow d \land \neg a$$ (Morgan law)
Therefore $$a$$ is strictely false and $$d$$ is strictly True so that the $$\neg (\neg d \lor a)$$ proposition is True.
Also in: $$a\lor \neg b$$ We conclude that $$\neg b$$ is True so $$b$$ is False (knowing that $$a$$ is False) so that the proposition $$a \lor \neg b$$ is True.
In: $$c \rightarrow b$$. We have $$b$$ False, so for the $$c \rightarrow b$$ proposal to be True $$c$$ must be strictly False to satisfy the proposal.
The statement $$(\neg a \land c) \lor d$$ is also True with all our results.

That evaluation of: $$a$$, $$b$$, and $$c$$ are false, and $$d$$ it true, satisfies all of the propositions.