Question

In a certain code language, "^" means "is less than", "#" means "is greater than" and "*" means "is equal to". Given that \(a^b\), \(c^d\), and \(c#b\), then which of the following is most definitely true?

• A. $a\char`^b\char`^c$
• B. a#b#c
• C. $d\char`^a$
• D. a*c
• E. b#d

Hint:

In coding-decoding problems, carefully translate symbols and then chain inequalities.

Answer 1

Answer: (E)

Step 1: Decoding Symbols:
"^" means "is less than" (we'll use \( < \))
"#" means "is greater than" (we'll use \( > \))
"*" means "is equal to" (we'll use \( = \))
Given: aᵇ, cᵈ, and c#b.
This means: a < b, c < d, and c > b.

Step 2: Establishing Relationships:
From c > b and a < b, we get: c > b > a.
From c < d, we get: d > c > b > a.
So, d > b.

Step 3: Converting to Code:
d > b means d is greater than b, which in code is d#b.
But option (E) is b#d, which means b > d. That is the opposite.
Option (A) aᵇᶜ means a < b < c, which is definitely true.

Final Answer: Option (A)