Mathematics: Find a counterexample to show that the following statement is false. for all sets a and b, (a ∪ b)c = ac ∪ bc. assume that all sets are subsets of a universal set u = {1, 2, 3, 4, 5}. (enter your answer as a comma-separated list in the form a, b where both a and b are written in set-roster notation. enter empty or ∅ for the empty set.)

Find a counterexample to show that the following

tasjanayroberts

08.01.2022

Given,

The universal set,

U = {1, 2, 3, 4, 5},

Let A = {1, 2},

B = {2, 3, 4}

$A\cup B=\text{ all elements of A and B }=\{1, 2, 3, 4\}$

$(A\cup B)^c=U-(A\cup B) = \{1, 2, 3, 4, 5\} - \{1, 2, 3, 4\} = \{5\}$

Now,

$A^c = U - A = \{3, 4, 5\}$

$B^c=U-B=\{1, 5\}$

$A^c\cup B^c = \{1, 3, 4, 5\}$

$\implies (A\cup B)^c\neq A^c\cup B^c$

Hence, proved......

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