Consider rolling a sixsided die Let A be the set of outcomes

Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number. Let B be the set of outcomes where the roll is greater than 3. Calculate and compare the sets on both sides of De Morgan’s laws

Solution

Here,

A = {2,4,6}
B = {4,5,6}

Thus,

(A U B)c = {2,4,5,6}c = {1,3}

Ac and Bc = {2,4,6}c and {4,5,6}c = {1,3,5} and {1,2,3} = {1,3} [they are equal!]

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(A and B)c = [{2,4,6}and{4,5,6}]c = {4,6}c = {1,2,3,5}

Ac U Bc = {1,3,5}U{1,2,3} = {1,2,3,5} [they are equal!]