We are given the following pair of true statements.
&1. If a=3, then 5a=15.
&2. If 12a=1 12, then a=3.
We are asked to use the Law of Syllogism to write a new conditional statement that follows from the given pair of statements. Let's start by recalling the Law of Syllogism.
&1. If hypothesis p, then conclusion q. [0.5em]
&2. If hypothesis q, then conclusion r.
&3. If hypothesis p, then conclusion r.
According to this law, if the first and the second statements are true, then the third statement is true. Now we can take a closer look at the given two conditional statements. Let's do it!
&1. If a=3, then 5a=15.
&2. If 12a=1 12, then a=3.
Notice that the conclusion of the second statement is the hypothesis of the first statement. The order in which the statements are given does not affect whether we can use the Law of Syllogism. This means that we can write the following new statement.
&3. If 12a=1 12, then 5a=15.
