Final answer:
The correct conditional sentence for 'q → s' is 'If q is true, then s is true.' Its truth value is true if s is true whenever q is true. To find the truth value, we must know the actual truth of q and s.
Step-by-step explanation:
A conditional statement is expressed in the form 'If p, then s' which means that s is true whenever p is true. The truth value of a conditional depends on the actual truth of its components, the antecedent (p) and the consequent (s). Here are the options rewritten as conditional sentences and their corresponding truth values:
- A. If q is true, then s is true. True if whenever q happens to be true, s is also true; otherwise, False.
- B. If s is true, then q is true. This does not relate to the conditional q → s, so it's not informative about the truth value of q → s.
- C. If q is false, then s is true. This statement is also not a correct expression of the conditional q → s, as the conditional does not claim anything about the scenario when q is false.
- D. If s is false, then q is false. This is an example of the contrapositive of the original conditional q → s, which is logically equivalent. So, if the original conditional is true, then this is also True.
It is important to understand that in a conditional statement, the antecedent is the first part after 'if' and the consequent is the second part after 'then'. To determine the truth value, one must look at the actual truth of the antecedent and consequent. For example, in the statement 'If it is rainy, then the ground is wet', the truth value is considered True if every time it rains, the ground does indeed get wet.