Prove that

For all sets A and B, A∩ (A∪B) = A.

A∩ (A∪B) = A

Step-by-step explanation:

Let's find the answer as follows:

Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:

A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:

A∪B = (X1≤A≥X2) ∪ (Y1≤B≥Y2)

Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.

With this in mind, A∩ (A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2) ∪ (Y1≤B≥Y2), which are:

A∩ (A∪B) = (X1≤A≥X2) which gives:

A∩ (A∪B) = A