Question

Given below are three statements, based on which some conclusions have been drawn. If the statements are TRUE, which of the conclusions can be said to be TRUE?
Statement 1: Visuals can either be abstract or non-abstract.
Statement 2: All logos are abstract visuals.
Statement 3: All photographs are non-abstract visuals.

• A. A logo cannot be a photograph.
• B. A photograph cannot be a logo.
• C. An abstract photograph can be a logo.
• D. A non-abstract logo can be a photograph.

Hint:

For syllogism and logical deduction problems, visualizing the relationships using Venn diagrams or set notation can make the premises much clearer and help you avoid errors in reasoning.

Answer 1

The Correct Option is A, B

Step 1: Understanding the Concept:
This is a logical deduction problem based on a set of premises (the statements). We can model the statements using set theory. Let V be the set of all visuals, A be the set of abstract visuals, and N be the set of non-abstract visuals. Let L be the set of logos and P be the set of photographs.
Step 2: Key Formula or Approach:
From the statements, we can establish the following relationships: 1. V = A \(\cup\) N, and A \(\cap\) N = \(\emptyset\) (The sets of abstract and non-abstract visuals are mutually exclusive and exhaustive). 2. L \(\subseteq\) A (The set of logos is a subset of abstract visuals). 3. P \(\subseteq\) N (The set of photographs is a subset of non-abstract visuals).
Step 3: Detailed Explanation:
From our setup, since all logos are in set A (abstract) and all photographs are in set N (non-abstract), and sets A and N are disjoint (have no elements in common), it logically follows that the set of logos (L) and the set of photographs (P) must also be disjoint. L \(\cap\) P = \(\emptyset\).
Now let's evaluate the conclusions:
A. A logo cannot be a photograph. This is true. Since the set of logos and the set of photographs are disjoint, no object can be both a logo and a photograph.
B. A photograph cannot be a logo. This is also true. It's the same conclusion as A, stated differently.
C. An abstract photograph can be a logo. This is false. Statement 3 says ALL photographs are non-abstract. Therefore, an "abstract photograph" cannot exist according to the premises.
D. A non-abstract logo can be a photograph. This is false. Statement 2 says ALL logos are abstract. Therefore, a "non-abstract logo" cannot exist according to the premises.
Step 4: Final Answer:
The only conclusions that can be drawn as TRUE are A and B.