Question

Verify whether the following statement is true or false. Why?

1)\[\left\{ x:x+3=3 \right\}=\varphi \]

Answer 1

Hint: Find the solution set by finding the number of values of x for which the given equation satisfies, then compare it and say whether the statement is true or false.

Complete step-by-step answer:
In the question we are given a set form of \[\left\{ x:x+3=3 \right\}\] and it is said that its value is equal to { }. Now we have to tell if it is true or false.

At first we will briefly understand what is set.

In mathematics sets is a well defined collection of distinct objects, considered as an object in its own right. The arrangement of the objects in the set does not matter. For example, the numbers 2, 4, 6 are distinct and considered separately, but they are considered collectively they form a single set of size three written as {2, 4, 6} which could also be written as {2, 6, 4}.
The set builder form given, means that a set of values x is the solution set if it satisfies the equation, \[x+3=3\].

Now we will solve \[x+3=3\]. So, only one value satisfies which is 0.

So, the solution set is {0}, which is not the same as { }.

Hence, the given statement is false.

Note: Students generally confuse between {0} and null sets, as the former say that there is a set with one element which is 0 but the latter says that there are no elements in the set.