The statements p → q and q → r are given. If we know q is true, is p necessarily true? Explain.?
no. The converse is unknown.
To answer this question, we need to understand the concept of implication in logic.
In logic, the statement "p → q" means that if p is true, then q must also be true. It implies that if the condition p is satisfied, it guarantees the truth of q.
Now, let's consider the given statements: p → q and q → r. We know that q is true.
If q is true, according to the second statement (q → r), it implies that r must also be true. So, we can conclude that r is true.
However, having the information that q is true does not provide us with any information about the truth value of p. The statement p → q doesn't tell us anything about whether p is true or false.
Therefore, we cannot infer whether p is necessarily true or false based solely on the information that q is true. The truth value of p could be either true or false, and we don't have enough information to determine its truth value.