I honestly need help on this question.
Determine whether statement(3)follows from statements(1)and(2)by the law of detachment or law of syllogism.If it does,state which law was used.If it does not,write invalid.
(1)If n is an integer,then n is a real number.
(2)n is a real number.
(3)n is an integer.
does not follow.
To determine whether statement (3) follows from statements (1) and (2) by the law of detachment or the law of syllogism, we first need to understand these logical laws.
1. Law of Detachment: If we have a conditional statement in the form "If p, then q" and we know that p is true, we can conclude that q is also true. In other words, if the "if" part is true, we can infer that the "then" part is true.
2. Law of Syllogism: If we have two conditional statements in the form "If p, then q" and "If q, then r," we can combine them to conclude "If p, then r." In other words, if we have an intermediate step where the "then" part of one statement becomes the "if" part of another statement, we can make a direct connection between the initial "if" part and the final "then" part.
Now let's analyze the problem using these laws:
Statement (1): If n is an integer, then n is a real number.
Statement (2): n is a real number.
To use the Law of Detachment, we need a conditional statement in the format "If p, then q" where p is a true statement that matches the assumption we have. In this case, we can observe that statement (1) matches this requirement. It states that if n is an integer (which is a true statement), then n is a real number. Therefore, we can use the Law of Detachment in this case.
Using the Law of Detachment, we can conclude that if n is an integer, then n is a real number (Statement (1)). Since statement (2) says that n is a real number, we can derive that n is an integer (Statement (3)).
Therefore, by using the Law of Detachment, statement (3) follows from statements (1) and (2).