Question

It is given that
\(\times\) denotes greater than,
\(\phi\) denotes equal to,
\(<\) denotes not less than,
\(\perp\) denotes not equal to,
\(\Delta\) denotes less than,
\(+\) denotes not greater than.
Choose the correct statement from the following-
If a \(\times\) b \(\Delta\) c it follows that-

• A. a \(\phi\) c \(\Delta\) b
• B. b \(<\) a \(\times\) c
• C. a \(<\) b \(+\) c
• D. c \(+\) b \(<\) a

Hint:

Always simplify "not less than" (\(\not<\)) to "greater than or equal to" (\(\ge\)) and "not greater than" (\(\not>\)) to "less than or equal to" (\(\le\)) immediately. It avoids double-negative confusion during calculations.

Answer 1

The Correct Option is C

Step 1: Build the symbol key.
$\times$ is $>$, $\phi$ is $=$, $\perp$ is $\neq$, $\Delta$ is $<$, and $+$ is $\le$ (not greater than).
Step 2: Decode the given statement.
$a \times b \Delta c$ becomes $a>b$ and $b<c$.
Step 3: Note what we can rely on.
We firmly know $a>b$ (so $a\ge b$ holds) and $b<c$ (so $b\le c$ holds).
Step 4: Test the options for a guaranteed truth.
Any option claiming $b\ge a$ contradicts $a>b$, and any option forcing $a=c$ is not certain, so those drop out.
Step 5: Find the safe option.
The choice that reads $a\ge b$ and $b\le c$ is fully backed by the given facts.
Step 6: Conclude.
Option (C) is the statement that must follow.
\[ \boxed{\text{Option (C): } a \ge b \text{ and } b \le c} \]