ych22 said:"Every student in this class has studied calculus".
Q(x): x is in this class.
P(x): x has studied calculus.
How come we have Q(x)->P(x) but not Q(x) ^ P(x)? What really is the difference?
A conditional proposition is a statement that follows an "if-then" structure, where the truth of the first part (the "if" statement) determines the truth of the second part (the "then" statement). It can also be written as "if p, then q" or "p implies q".
The two parts of a conditional proposition are the "antecedent" or "if" statement, and the "consequent" or "then" statement. The antecedent is the condition or situation that must be true in order for the consequent to be true.
The truth value of a conditional proposition depends on the truth values of its antecedent and consequent. If the antecedent is true, then the consequent must also be true for the entire proposition to be true. If the antecedent is false, then the truth value of the proposition is irrelevant.
A conditional proposition is a statement that follows an "if-then" structure, while a biconditional proposition is a statement that follows an "if and only if" structure. In other words, a biconditional proposition is true only if both the antecedent and consequent are true, while a conditional proposition can still be true if the antecedent is false.
Conditional propositions are used in scientific research to form hypotheses and make predictions about the relationship between different variables. By stating a conditional proposition, scientists can test whether certain conditions (the antecedent) lead to specific outcomes (the consequent), and use this information to draw conclusions and make scientific discoveries.