Discrete Mathematics · Propositional and predicate logic with proof methods

Let A={1,2,3,4} and B={3,4,5,6}

Problem

Let \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\). Compute, by listing elements, each of the following sets: \[ A\cup B,\quad A\cap B,\quad A\setminus B,\quad B\setminus A,\quad A\triangle B,\quad\text{and}\quad\mathcal{P}(A\cap B), \] where \(\triangle\) denotes symmetric difference and \(\mathcal{P}\) denotes the power set.

Hint

Union is “in at least one,” intersection “in both,” difference “in the first but not the second,” and symmetric difference is the union of the two directed differences.

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