By Howard Anton; Bernard Kolman

Reasonable and proper functions from quite a few disciplines aid inspire company and social technology scholars taking a finite arithmetic path. a versatile enterprise permits teachers to tailor the publication to their path

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The reason equality does not hold is clear from this example. The element d n(A) and once again d i s counted twice in computing is counted once in computing so that the element in computing n(B), n(A) + n(B) . On the other hand, the element d is only counted once in computing n(A u B). This example suggests the following idea. Suppose joint. W e know that we cannot simply add n(A u B) n(A) A B are not dis n (B) to obtain in A n B twice. 4 COUNTING ELEMENTS IN SETS I 33 Since we only want to count these elements once, we can correct for this duplication by subtracting n(A n B) once.

A) A = { x I x is a consonant in the English alphabet} . (b) A = { x I x is a solution of x2 = 1 } . (c) A = {3, - 2, 5, 9} . , i, c, k, l, e l . (e) A = { x I x is an even integer! (f) A = { x I x s i a real number satisfying x2 = -4} . 2. Verify the equation n(A U B) = n(A) + n(B) for the following disjoint sets (a) A = { a, e, f, z } and B = { c, h, k } . (b) A = { x I x is a real number satisfying x2 < O } and B = { x I x is a real number satisfying x2 = 4} . 3. If A and B are disjoint sets such that n(A U B) = n(A) , what can we say about B?

I, c, k, l, e l . (e) A = { x I x is an even integer! (f) A = { x I x s i a real number satisfying x2 = -4} . 2. Verify the equation n(A U B) = n(A) + n(B) for the following disjoint sets (a) A = { a, e, f, z } and B = { c, h, k } . (b) A = { x I x is a real number satisfying x2 < O } and B = { x I x is a real number satisfying x2 = 4} . 3. If A and B are disjoint sets such that n(A U B) = n(A) , what can we say about B? 4. Verify the equation n(A U B) = n(A) + n(B) - n(A nB) for the following sets.