Question

If a and b are integers and \[a\ne b\], then which of the following is incorrect?
a) a + b = b + a
b) a - b = b - a
c) a + 0 = 0 + a = a
d) \[a-0=a\ne 0-a\]

Answer 1

Hint: In this type of question when we know two different variables who are integers and not equal and we need to find which of the relation is wrong among the following we will first assume on which number is bigger and which one is smaller then we will be easily able to decide which of the relation mentioned in the question is wrong.

Complete step by step solution:
In the above type of question we need to first assume out of the two integers which of them is greater so as to make our question easier to solve. Let us assume that a is greater than b now from the following statements/ relation we will use our assumed basis to come to a result.
So in option (a) we have been given a relation in which addition is taking place between the two integers on both the sides of the equation as it is addition the magnitude and the sign will be the same so this is a correct option.
Now in option (b) we can see that on RHS the bigger variable is being subtracted from smaller and vice versa on LHS so we can conclude that this option is wrong as the sign will be different on both the sides of the equation so this relation is the incorrect one.
If we consider options (c) and (d), it deals with a and both the equations hold true.
So from above we can conclude that option (b) is the incorrect relation.

So, the correct answer is “Option B”.

Note: In this type of question always assume a greater number when it is not mentioned in the question that will help us find the correct option among the four options available in a faster way like in the above it was mentioned that the two integers were not equal which signifies that one of the integer has to be greater than the other by using this we came to find the perfect answer.