Limited Common Elements

Limited common elements are elements that are common to two sets but not shared by a third set.

Definition:

For three sets A, B, and C, the limited common elements of A and B with respect to C are the elements that are common to A and B but not to C.

Formula:

Limited common elements (A and B with respect to C) = A ∩ B – C

Explanation:

1. A ∩ B: Find the common elements between sets A and B.
2. C: Subtract the elements of set C from the common elements.
3. Limited common elements: The remaining elements are the limited common elements.

Example:

Set A = {1, 2, 3, 4, 5}Set B = {2, 3, 4, 5, 6}Set C = {3, 4, 5, 7}

Limited common elements (A and B with respect to C) = {2, 3, 4, 5} – {3, 4, 5, 7} = {2}

Therefore, the limited common elements of A and B with respect to C are only the element 2.

Additional Notes:

• The limited common elements are always a subset of the common elements.
• If the third set C is empty, the limited common elements are equal to the common elements.
• The limited common elements can be used to find elements that are common to two sets but not to a third set.