Consider the proposition Every set has at least one subset 1

Consider the proposition \"Every set has at least one subset.\"

1. Prove this false proposition by counterexample.

Solution

The proposition has some ambiguity since every set is its own subset.

Hence wording should be every set has atleast one proper subset.

Consider the null set phi.

This set has no proper subset hence the proposition that every set has atleast one proper subset.is not true.