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Eg. : If A = {1, 2, 3}

B = {3, 4, 5}

Then A - B = {1, 2}

Also, B – A = {4, 5}

∴ AΔB = (A-B) ∪^ (B-A)

= {1, 2, 4, 5}

27. Cartesian product of two sets
    If A and B are two sets, a set of ordered pairs can be formed associating every
    element of A as the first component and every element of B as the second
    component. The set of such ordered pairs is called the Cartesian product or Cross
    product and is denoted as A×B.

Eg. : Let A = {1, 2}

B = {3,4}

Then, A ×^ B = { (1,3), (1,4), (2,3), (2,4) }

Note : In general, if n(A) = p and n(B) = q, then n(A × B) = pq

28. An identity in set language
    If A and B are any two non-empty overlapping sets, then

n(A ∪^ B) = n(A) + n(B) – n( A ∩^ B)

Note that if A and B are non-overlapping(disjoint) sets, then n(A ∪^ B) = n(A) + n(B)

The methods used in the previous examples may also be adopted in the case of

identity in set language.