Twenty-five different beauty products make the following claim: 13 claims for whitening the skin, 20 claims to soften the skin, 11 claims to reduce wrinkles, 8 claims to both whitening and softening the skin, 5 claims to both whitening and reducing wrinkles, and 6 claims to both softening the skin and reducing the wrinkles.
(i) Give a suitable name for the sets. Indicate the cardinality of each set. Determine and propose set operations that can be performed on the sample data above. Justify your reasons for proposing the set operations.
(ii) Create Venn diagram to represent the set operations that you derive from Question (i) above. Analyze the Venn diagram and state the conclusion that you can derive from the Venn diagram.
(iii) Analyze how many products make all three claims. Justify your answer.
(iv) Analyze how many products claim for whitening the skin but do not claim to reduce wrinkles. Justify your answer.
(v) Give another example of how sets can be applied to group objects or elements together. Support your answer by providing detailed explanation.