When a solution set is empty?

If an equation has no solutions, its solution set is the empty set or null set–a set with no members, denoted Ø. For example, the solution set to x² = – 9 is Ø, because no number, when squared, is equal to a negative number.

What does it mean for a set to be empty?

having no elements

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

What does it mean when a solution has no solution?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

What if the solution set is 0?

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation.

How do you prove a set is empty?

This is essentially a proof by contraction. In a proof by contradiction, you assume some assertion P is true, and then deduce a contradiction from it. You may then conclude P is false, as if it were true, a statement known to be false would be true. To prove the set A is empty, begin by assuming A is non-empty.

What is an empty set give an example?

Any Set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ. Examples: Let A = {x : 9 < x < 10, x is a natural number} will be a null set because there is NO natural number between numbers 9 and 10.