Question

If \( X' \) stands for addition, \(<\) for subtraction, \( + \) for division, \(>\) for multiplication, \( - \) for equal to, \( + \) for greater than, and \( = \) for less than, then state which of the following option is true?

• A. \( 3 \times 4>2 - 9 + 3<3 \)
• B. \( 5 \times 3<T7 + 8 + 4 = 1 \)
• C. \( 5>2 + 2 = 10<4 = 8 \)
• D. \( 3 \times 2<4 + 16>2 + 4 \)

Hint:

Carefully analyze the given operations and evaluate each expression step by step.

Answer 1

The Correct Option is C

We are given that the symbols represent different operations as follows:
- \( X' \) stands for addition,
- \(<\) stands for subtraction,
- \( + \) stands for division,
- \(>\) stands for multiplication,
- \( - \) stands for equal to,
- \( + \) stands for greater than,
- \( = \) stands for less than.
Step 1: Interpreting the symbols in each option:
- In option (A):
\( 3 \times 4>2 - 9 + 3<3 \),
which is \( 3 \times 4 \, \text{(multiplication)} \,>\, 2 - 9 + 3 \, \text{(subtraction)} \,<\, 3 \). On simplification, this gives a false equation.
- In option (B):
\( 5 \times 3<T7 + 8 + 4 = 1 \),
which is also false as the operation is incorrect.
- In option (C):
\( 5>2 + 2 = 10<4 = 8 \),
this simplifies to true when operations are performed, satisfying the conditions.
- In option (D):
\( 3 \times 2<4 + 16>2 + 4 \),
this also gives a false equation.
Step 2: Verifying option (C):
When interpreting \( 5>2 + 2 = 10<4 = 8 \), it simplifies to true when the correct operations are performed. Hence, option (C) is the correct answer.