Question

In a certain code language, ‘^’ means ‘is less than’, ‘#’ means ‘is greater than’ and ‘*’ means ‘is equal to’ and given that a^b, c*d, and c#b, then which of the following is true?

• A. d^a
• B. b#d
• C. a*c
• D. a^b^c

Answer 1

The Correct Option is D

To solve this question, we need to interpret the given statements based on the code language provided:

• The symbol '^' means 'is less than'. Therefore, 'a^b' translates to 'a is less than b'.
• The symbol '*' means 'is equal to'. Therefore, 'c*d' translates to 'c is equal to d'.
• The symbol '#' means 'is greater than'. Therefore, 'c#b' translates to 'c is greater than b'.

Given these conditions:

• a < b 
• c = d
• c > b

We need to determine which option is true based on the given information.

1. Option 1: d^a. Since c = d and c > b, but nothing is directly given about the relationship between d and a.
2. Option 2: b#d. Here, since c = d and c > b, b < c means b < d, so b#d is false.
3. Option 3: a*c. Since a < b and c > b, this means a < c, so a is not equal to c.
4. Option 4: a^b^c. This option is a chain relationship. Given a < b and b < c (because c > b), it can be inferred that a < b < c. Thus, a^b^c holds true.

From the above reasoning, the correct answer is the fourth option: a^b^c. This sequence maintains the consistency of inequalities derived from the initial conditions.