The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'

  a)  {5, 6}

  b)  {2, 3, 4, 5, 6, 7, 8, 9}

  c)  {0, 1, 7, 8, 9}

  d)  {0, 1, 2, 3, 4}

Step-by-step explanation:

The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.

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  {2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}

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  {2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}

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  U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}

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  U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}

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step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)