Final answer:
The statement is true based on the principle of material implication.
Step-by-step explanation:
The truth value of the statement "If circles have 180 degrees or even numbers are multiples of 3, then triangles have 3 vertices" can be determined by examining the statement itself. In this case, we can see that the statement is a conditional statement, which means that it is in the form "If A, then B". To determine if the statement is true or false, we need to evaluate whether the condition (A) is true and whether the conclusion (B) is true.
Looking at the condition, we have two parts: "circles have 180 degrees" and "even numbers are multiples of 3". Both of these parts are false because circles do not have 180 degrees (they have 360 degrees) and even numbers are not always multiples of 3. Since the condition is false, we don't need to evaluate the conclusion, and we can conclude that the entire statement is true based on the principle of material implication.