Sets

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Step 1: List the multiples of 3 less than 20. Step 2: They are 3, 6, 9, 12, 15, 18. Step 3: Write them in braces. Answer: A = {3, 6, 9, 12, 15, 18}.

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Formula: Q = {x : x = (p)/(q), p, q are integers and q != 0}. Meaning: Every rational number can be written as a fraction of two integers, with non-zero denominator. Quick example: (5)/(6) and (-3)/(4…

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Step 1: A set does not repeat elements. Step 2: The letters in SCHOOL are s, c, h, o, o, l. Step 3: The repeated letter o is written only once. Answer: {s, c, h, o, l}.

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Step 1: Compare the elements in both sets. Step 2: Both contain 1, 2, 7, and 9. Step 3: The order changes, but the elements do not change. Answer: The two sets are equal because roster form ignores or…

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Step 1: { } has no elements. Step 2: {0} has one element, namely 0. Step 3: Since the number of elements is different, the sets are different. Answer: They are different sets.

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Step 1: Take elements of A that are not in B. Step 2: In A, 4 and 5 are also in B, so remove them. Step 3: Remaining elements are 1, 2, 3. Answer: A - B = {1, 2, 3}.

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Step 1: Take elements of B that are not in A. Step 2: 4 and 5 are in A, so remove them. Step 3: Remaining elements are 6 and 7. Answer: B - A = {6, 7}.

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Step 1: Find A - B = {1, 2, 3}. Step 2: Find B - A = {6, 7}. Step 3: Compare the two results. Answer: They are different, so A - B != B - A in general. Order matters in set difference.