If `cap` stands for '+', `sub` stands for '-', `sup` stands for 'x', `cup` stands for'+', '||' stands for '=' and `to` stands for `gt`, then which of the following expressions is not true ?

Options

A. `(10 cap 2) sup (2 cap 2) to (10 cup 2)`
B. `(20 sub 8) cup (4 sub 1) || (4 cap 1)`
C. `(12 sub 4) sup (5 sup 1) to (10 cap 20)`
D. `(10 cap 2) sup (2 cup 2) to (10 cup 2)`

Answer

To solve the problem, we need to decode the symbols and evaluate the expressions given in the options. Let's go through the steps one by one.

### Step 1: Decode the Symbols
The symbols are defined as follows:
- `cap` stands for `+`
- `sub` stands for `-`
- `sup` stands for `x`
- `cup` stands for `+`
- `||` stands for `=`
- `to` stands for `gt`

### Step 2: Evaluate Each Expression
We will evaluate each option to find which one is not true.

#### Option 1:
Expression: `10 cap 2 sup 4 to 10 sub 5`
- Decode: `10 + 2 x 4 > 10 - 5`
- Calculate:
- Left side: `10 + (2 x 4) = 10 + 8 = 18`
- Right side: `10 - 5 = 5`
- Check: `18 > 5` is true.

#### Option 2:
Expression: `20 sub 8 cup 4 sup 1 || 4 cap 1`
- Decode: `20 - 8 + 4 x 1 = 4 + 1`
- Calculate:
- Left side: `20 - 8 + (4 x 1) = 12 + 4 = 16`
- Right side: `4 + 1 = 5`
- Check: `16 = 5` is not true.

#### Option 3: (Assuming there is a third option)
Expression: `15 sup 3 sub 5 cup 2 || 10 cap 5`
- Decode: `15 x 3 - 5 + 2 = 10 + 5`
- Calculate:
- Left side: `(15 x 3) - 5 + 2 = 45 - 5 + 2 = 42`
- Right side: `10 + 5 = 15`
- Check: `42 = 15` is not true.

### Conclusion
From the evaluations, we found that the second expression is not true.

### Final Answer
The expression that is not true is Option 2: `20 sub 8 cup 4 sup 1 || 4 cap 1`.

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