Chapter 1, Problem 1RE

To determine

The solution set for a contradiction.

Answer to Problem 1RE

Solution:

The solution set of a contradiction is the empty set $\left\{\right\}$ .

Explanation of Solution

For example, we have the equation

  $10x-21=2(x-5)+8x$

After solving some steps of the equation we see the terms of x will be cancelled from both the sides of the equation and we will get a false statement.

  $10x-21=2x-10+8x$

  $10x-21=10x-10$

  $-21=-10$

So, here we can say that after solving the equation, we will not get any solution.

Conclusion:

Hence, if we solve a contradiction equation, there will be no solution. That is, solution set of a contradiction is the empty set $\left\{\right\}$ .