In Example 2, "The sun is made of gas" is the hypothesis and "3 is a prime number" is the conclusion. Note that the logical meaning of this conditional statement is not the same as its intuitive meaning. In logic, the conditional is defined to be true unless a true hypothesis leads to a false conclusion. The implication of a b is that: since the sun is made of gas, this makes 3 a prime number. However, intuitively, we know that this is false because the sun and the number three have nothing to do with one another! Therefore, the logical conditional allows implications to be true even when the hypothesis and the conclusion have no logical connection.