2) Prove the conjecture, from the set of statements. First write the statements inlogical form, and from them, prove the conjecture. The universe is orderly (like awatch that follows complex laws). Most orderly things we’ve examined haveintelligent designers. We’ve examined a large and varied group of orderly things. Ifmost orderly things we’ve examined have intelligent designers and we’ve examineda large and varied group of orderly things, then probably most orderly things haveintelligent designers.Conjecture: If the universe is orderly, then it has an intelligent designer

To prove the conjecture, we need to follow a step-by-step approach. Let's first write the statements in logical form:

1. The universe is orderly (U).
2. Most orderly things we've examined have intelligent designers (M).
3. We've examined a large and varied group of orderly things (E).

Now, let's use these statements to prove the conjecture:

1. If most orderly things we've examined have intelligent designers (M) and we've examined a large and varied group of orderly things (E), then probably most orderly things have intelligent designers (P).

2. We can rewrite this statement as: (M ∧ E) → P.

3. Now, we can use the concept of modus ponens to prove the conjecture. Modus ponens states that if we have a conditional statement (A → B) and we know that A is true, then we can conclude that B is true.

4. In our case, we have (M ∧ E) → P. We know that (M ∧ E) is true because both statements M and E are true.

5. Therefore, using modus ponens, we can conclude that P is true. In other words, if most orderly things we've examined have intelligent designers and we've examined a large and varied group of orderly things, then probably most orderly things have intelligent designers.

6. Thus, we have proven the conjecture: If the universe is orderly (U), then it has an intelligent designer.