All the following are properties of natural number N, for a and b belonging to N, except*1 pointa*ba + ba < ba - b

The statement "a*ba + ba < ba - b" is not a property of natural numbers.

Here's why:

Step 1: Understand the statement The statement is saying that for any two natural numbers a and b, the sum of a*ba and ba is less than the difference of ba and b.

Step 2: Test the statement with an example Let's take a = 2 and b = 3. According to the statement, 2*23 + 23 should be less than 23 - 3.

Step 3: Calculate 2*23 + 23 = 46 + 23 = 69 23 - 3 = 20

Step 4: Compare 69 is not less than 20.

Therefore, the statement "a*ba + ba < ba - b" is not a property of natural numbers.

The statement "a*ba + ba < ba - b" is not a property of natural numbers.

Here's why:

Let's break it down:

1. a*ba + ba: This is simply multiplication and addition of natural numbers, which will always result in another natural number.

2. ba - b: This is multiplication and subtraction of natural numbers. As long as "b" is not greater than the product of "b" and "a", this will result in a natural number.

However, the inequality states that "a*ba + ba" (which will always be a larger number because we're adding positive numbers) is LESS THAN "ba - b" (which will always be a smaller number because we're subtracting).

This contradicts the basic properties of natural numbers, where if you add to a number, it gets larger, and if you subtract, it gets smaller. Therefore, the statement "a*ba + ba < ba - b" is not a property of natural numbers.

The statement "a + b < a - b" is not a property of natural numbers.

Here's why:

Step 1: Understand the statement The statement is saying that for any two natural numbers a and b, the sum of a and b is less than the difference of a and b.

Step 2: Test the statement with an example Let's take a = 5 and b = 3, both of which are natural numbers. According to the statement, 5 + 3 should be less than 5 - 3.

Step 3: Evaluate the example 5 + 3 equals 8, and 5 - 3 equals 2. 8 is not less than 2, so the statement is false.

Step 4: Conclusion Since the statement is false for these natural numbers, it's not a property of natural numbers. Natural numbers are always non-negative, so the sum of two natural numbers can never be less than their difference.