Consider the statements: p: Stephen is intelligent q: Stephen is good at Mathematics If p⇒q, which of the following is a valid conclusion?

Answer Details

The given statements are: - p: Stephen is intelligent - q: Stephen is good at Mathematics The symbol "⇒" means "implies". So, p⇒q means "if Stephen is intelligent, then he is good at Mathematics". , "If Stephen is good at Mathematics, then he is intelligent", is a valid conclusion because it is the contrapositive of p⇒q. In other words, if the original statement is true, then its contrapositive must also be true. The contrapositive of p⇒q is "if Stephen is not good at Mathematics, then he is not intelligent" However, is also valid because the contrapositive of a true statement is always true. , "If Stephen is not intelligent, then he is not good at Mathematics", is the inverse of the original statement and is not necessarily true. In other words, just because Stephen is not intelligent, it does not mean that he is not good at Mathematics. For example, he may have a natural talent for Mathematics even if he is not generally intelligent. , "If Stephen is not good at Mathematics, then he is intelligent", is the converse of the original statement and is also not necessarily true. In other words, just because Stephen is good at Mathematics, it does not mean that he is intelligent. For example, he may be good at Mathematics but struggle with other subjects. So, the valid conclusion is: "If Stephen is good at Mathematics, then he is intelligent".