D = a decision
P = a piece of information
Q = another piece of information
a piece of information can change a decision, P → D
another piece of information can not change a decision, ¬(→)
Then both pieces of information together can change the decision?
(→)∧¬(→)
Is the statement true? I mean is below statement true,
Both pieces of information together can change the decision, D
Why Its creating confusion to me?
When a mind gets both piece of information, Things getting confused!
P = a piece of information
Q = another piece of information
So,
P ∧ Q = Both pieces of information together, thus
P ∧ Q → D = Both pieces of information together can change the decision
But,
(P → D) ∧ ¬(Q → D) is not same as (P ∧ Q), right?
Anyone can clarify what am I missing?
This ultimately depends on interpretation, especially if this is not a question about strict rules of logic, but instead a question about practical decision making.
The difference between $P\land Q\to D$ and $(P\to D)\land \lnot(Q\to D)$ is that (translated in your words) the first states that "the information of $P$ and $Q$ together will change the decision", while the second states "the information of $P$ changes the decision, and the information of $Q$ does not".
From a propositional standpoint, this means that $P\land Q\to D$ is true whenever $D$ is true or either $P$ or $Q$ is not true. On the other hand, $(P\to D)\land \lnot(Q\to D)$ is true whenever $P\to D$ is true (i.e. $P$ is false or $D$ is true) and $Q\to D$ is false (i.e. both $D$ is true and $Q$ is false).
In particular, we see that the second sentence needs $D$ to be true, while the first one does not.
However, as this is about information changing a decision, things should not really be interpreted using propositional logic. There is a clear causality between the events of $P$ and $Q$ becoming known and the making of the decision $D$, and this causality needs to be described properly.
The problem is that a decision does not have a truth value, but is an action instead. Similarly, although information can be true or false, the act of receiving new information is an action, and not a proposition.
Therefore, to properly model this kind of situation, I would consider using dynamic logic, or something similar.