Select the most appropriate meaning of the given idiom.

Beyond the shadow of a doubt

With certainty; for sure

The most appropriate meaning of the idiom "beyond the shadow of a doubt" is with certainty; for sure.

The other options are incorrect.

• Located in a remote area is not the same as with certainty. Being located in a remote area means being in a place that is far away from other people or places.
• Live in fear and uncertainty is not the same as with certainty. Living in fear and uncertainty means being worried and not knowing what is going to happen.
• Forget all past problems is not the same as with certainty. Forgetting all past problems means not thinking about them anymore.

The idiom "beyond the shadow of a doubt" comes from the idea of a shadow being a sign of doubt. In the same way, something that is beyond the shadow of a doubt is something that is certain and there is no doubt about it. For example, you might say that you know beyond the shadow of a doubt that your spouse loves you.