Is there a way to explain why this happens? Think of the rules for parity Class 8

Is there a way to explain why this happens? Think of the rules for parity Class 8

Question 1.

Is there a way to explain why this happens? Think of the rules for parity Class 8

Hint : Think of the rules for parity of the sum or difference of two numbers.

Solution:

Sum of two odd numbers is even.

Sum of two even number is even.

Further, in four consecutive numbers, two numbers will be odd and two numbers will be even.

Explanation 1: Let us consider any of the 8 expressions formed by four numbers a, b, c, and d. When one of its signs is switched, its value always increases or decreases by an even number! Let us see why.

Consider one of the expressions: a + b – c – d.

Replacing +b by – b, we get

a – b – c – d.

By how much has the number changed? It has changed by

(a + b – c – d) – (a – b – c – d)

= a + b – c – d – a + b + c + d (notice how the signs changed when we opened the second set of brackets)

= 2b (this is an even number).

If the difference between two numbers is even, can they have different parities? No! So either both are even or both are odd.

Now, let us see what happens when a negative sign is switched to a positive sign.