Below is a copy of a calendar for July 2015.

Statement: The sum of any two adjacent dates is always an even number. (Example of adjacent dates: 1 and 8, 22 and 29 etc)

Do it algebraically and check if the given statement is true or false.

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Solution

Let us consider any two adjacent dates.

If we take the first number which is as 'x', then number adjacent to this will be 'x + 7'.

Then the sum is

(x) + (x + 7) = 2x + 7

We note that 2x is a multiple of 2 and hence always an even number. When 7 is added to an even number, we get an odd number.

Hence the sum of any two adjacent dates in a calender is always an odd number.

Therefore the given statement is false.

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