Problem Set Theory 1 DM

A = {x ∣ x ∈ N, x is less than 20, and x is divisible by both 3 and 4} in word form.

Then, determine the set A in roster notation.

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Determine whether the sets A = {2,4,4,6,8,8} and B = {8,6,6,4,2,2} are equal.

Justify your answer.

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Write the set C = {5,6,7,8} using set-builder notation based on the examples provided.

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Problem: Let D = {1,3,5,7,9}. Determine if 2 ∈ D and 5 ∉ D.

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Determine whether the set E = {x ∣ x ∈ N and x>0} is finite or infinite.

Explain your answer.

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Set B is defined as {x ∣ x ∈ N,10 ≤ x < 20. Determine the cardinality of B.

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Set C is defined as {x ∣ x ∈ N, x ≤ 15, x ≠10. Find the cardinality of C.

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Convert the set G = {x ∣ x ∈ N and x<4} to roster notation.

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Set A is defined as {x ∣ x is a natural number less than 5 and greater than 10.

Determine whether A is an empty set. Explain your answer.

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Define set B as {x ∣ x is a square in two dimensions with three sides.

Determine whether B is an empty set.

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