‘This sentence is false’ is an example of what is known as the Liar Paradox.
This sentence is false.
Look at the first option for the answer—true. To do that, we check what the sentence says about itself. It says about itself that it is false. If it is true, then it is false, which is a contradiction, and therefore, the answer ‘true’ is not acceptable.
The second option is false. Since the sentence claims about itself as false, then it’s false that it’s false, which again is a contradiction.