Let a, b, and c be sets that are pairwise disjoint. (this means any pair of a, b, and c are disjoint. that is an b=), bac =), and anc = . is it true that aubuc| = a + b + c|? (compute some examples before trying to prove this.)

Answer and Step-by-step explanation:

Given:

A, B and C are the pairwise disjoint sets

To prove:

|A + B+ C| = |A| +|B| +|C|

Proof:

Since, A, B and C are the pairwise disjoint sets, therefore all the possible pairs of A, B and C will also be disjoint and these are:

;

;

;

;

;

;

Thus

;

|A\cap B\cap C| = 0

Now, lets take an example:

Suppose, A = {b, c, d}

B = {e, f, g}

C = {h, i}

Now, we know that:

Thus

|A + B+ C| = |A| +|B| +|C|

Hence proved

Now, we know that:

from the above established data, we can write that:

Hence, proved

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step-by-step explanation: