Set Theory - Let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Let se

Question

Set Theory -

Let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Let set P = {1,3,5,6,9}

Let set T = {2,3,4,5,7}

Let set W = {1,3,4,7,}

1. Find P T

A. {2,5}        B. {3,5}        C. {3,7}       D. {2,7}

2. Find T W

A. {1,2,3,4,5,7} B. {1,2,3,4,6,9} C. {1,2,7,8,9,10} D. {1,2,3,8,9,10}

3. Find T - P

A. {1,4,9} B. {1,4,8} C. {2,3,7} D. {2,4,7}

4. Find P'

A {2,4,5,8,10} B. {2,4,6,8,10} C. {2,4,7,8,10} D. {2,3,4,8,10}

5. Find W (T P)

A. {1,3,4,7} B. {1,3,5,7} C. {1,2,4,7} D. {2,3,4,7}

6. Find (T - W) (P W)

A. {4} B. {5} C. {7} D. {8}

7. find (T W)'

A. {1,2,4,6,8,9,10} B. {1,3,5,6,8,9,10} C. {1,2,5,6,8,9,10} D. {1,2,5,6,7,9,10}

Explanation / Answer

Given Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {1,3,5,6,9}, T = {2,3,4,5,7}, W = {1,3,4,7}

1) P T: Intersection of two sets A and B is the set contains all elements of A that also belongs to B (or) all elements of B that also belongs to A.

P T = {1,3,5,6,9} {2,3,4,5,7}

         = {3,5}

Answer: B

2) T W: Union of two sets A and B is the set contains all elements of both sets A and B.

T W = {2,3,4,5,7} {1,3,4,7,}

          = {1,2,3,4,5,7}

Answer: A

3) T - P: Relative complement: Elements that belongs to T but not to P

T - P = {2,3,4,5,7} - {1,3,5,6,9}

        = {2,4,7}

Answer: D

4) P': Complement: All the elements that do not belongs to set P.

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},

P = {1,3,5,6,9}

P' = {2,4,7,8,10}

Answer: C

5) W (T P)

T P = {2,3,4,5,7} {1,3,5,6,9}

          = {1,2,3,4,5,6,7,9}

W (T P) = {1,3,4,7} {1,2,3,4,5,6,7,9}

                   = {1,3,4,7}

Answer: A

6) (T - W) (P W)

T={2,3,4,5,7}, W={1,3,4,7}, P={1,3,5,6,9}

T - W = {2,5}

P W = {1,3,5,6,9} {1,3,4,7}

           = {1,3,4,5,6,7,9}

(T - W) (P W) = {2,5} {1,3,4,5,6,7,9}

                            = {5}

Answer: B

7) (T W)'

T={2,3,4,5,7}, W={1,3,4,7}

T W = {3,4,7}

(T W)' = T' W' (De-morgan's law)

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, T = {2,3,4,5,7}, W = {1,3,4,7}

T' = {1,6,8,9,10}, W'= {2,5,6,8,9,10}

T' W' = {1,2,5,6,8,9,10}

Answer: C

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