Question

Fact 1: All dogs like to run
Fact 2: Some dogs like to swim
Fact 3: Some dogs look like their masters
If the first three statements are facts, which of the following statement must also be a fact?
i) All dogs who like to swim look like their masters
ii) Dogs who like to swim also like to run
iii) Dogs who like to run do not look like their masters

• A. i only
• B. ii only
• C. ii and iii only
• D. none of them is a known fact

Hint:

When a premise states "All X are Y", then *any* subset of X you mention automatically belongs to Y. Since all dogs run, swimming dogs (which are a subset of dogs) must run too!

Answer 1

The Correct Option is B

Concept: This question requires us to apply categorical logic and deductive reasoning using the rules of syllogisms. We must treat the three initial statements as absolute, foundational facts and determine which of the subsequent statements can be logically deduced with absolute certainty.

Step 1: Analyzing the given facts.
Let us break down each given fact into logical sets: * Fact 1: "All dogs like to run." This means the set of "dogs who like to run" is entirely identical to the universal set of "All dogs". Every single dog in existence is included in this category. * Fact 2: "Some dogs like to swim." This indicates there is a subset of dogs that enjoy swimming. * Fact 3: "Some dogs look like their masters." This indicates there is another subset of dogs that look like their masters.

Step 2: Deductively evaluating statement (i).
* Statement (i): "All dogs who like to swim look like their masters." * Fact 2 and Fact 3 tell us that "some dogs swim" and "some dogs look like masters". However, there is no data establishing a mandatory connection between these two specific subsets. It is possible that the dogs who swim are entirely distinct from the dogs who look like their masters. Since this statement cannot be proven with absolute certainty, it is not a guaranteed fact.

Step 3: Deductively evaluating statement (ii).
* Statement (ii): "Dogs who like to swim also like to run." * From Fact 1, we know that every single dog likes to run. Therefore, any sub-category or subset of dogs you choose—whether it is dogs who like to swim, spotted dogs, or small dogs—must also like to run, because they are all dogs. Thus, the subset of "dogs who like to swim" must logically be contained within the universal set of "dogs who like to run". This statement is logically certain and must be a fact.

Step 4: Deductively evaluating statement (iii).
* Statement (iii): "Dogs who like to run do not look like their masters." * Fact 1 tells us all dogs like to run, and Fact 3 tells us some dogs look like their masters. Therefore, those "some dogs" who look like their masters *must* also like to run. Statement (iii) directly contradicts Fact 3 by asserting that running dogs do not look like their masters. Thus, statement (iii) is false. Reviewing our deductions, only statement (ii) is logically valid.