Sets and Functions Exercises 2.2

Today our topic of discussion is Sets and Functions Exercises 2.2.

Sets and Functions Exercises 2.2

 

 

Exercises 2.2

1. Which one is the set of factors of 8?

1) { 8, 16, 24 ,***}

3) (2,4,8)

2) (1,2,4,8}

4) {1,2}

2. If R is a relation from the set C to the set B, then which one of the following is true?

1) R ⊂ C

2) R ⊂B

3) R ⊆ CB * 4 )

C * B ⊆ R

3. If A = {1, 2} B = {2, 5} which one of the following is the number of elements of P( A ∩ B)?

1) 1

2) 2

3) 3

4) 8

4. Which one of the following expresses the set { x∈ N : 13 < x < 17 and z is

prime} in tabular method?

1) Ø

2) {0}

3) (0)

4){ 13, 17 }

5. If B = {a, b, c} , then

(i) A = {a, b} B = {a, b, c}

(ii) A = {a, b, c} B = {b, c}

(iii) A = {a, b} B = {c}

Based upon the above facts which one of the following is true?

1) i

2) ii

3) i and ii

4) i * ii and iii

6. If for two finite sets A and B

(1) A* B={(x,y):x in A and y∈ B}

(ii) If n(A) = a, n(B) = b , then n(AB) = ab

(iii) Each member of AB is an ordered pair.

Based upon the statements above which one of the following is true?

1) i and ii

3) ii and iii

2) i and iii

4) i, ii and iii

If A = {6, 7, 8, 9, 10, 11, 12, 13} , then answer the questions 7-9 below:

2) EN:6≤ <13)

7. Which one is the correct expression for the set A? 1) EN:6<<13) 3) \ x in N / 6 <= x <= 13 \

4) { x € N / 6 < x <= 13 }

8. Which one is the set of primes in A? 1) (6,8, 10, 12) 2) (7,9,11,13) 3) (7,11,13) 4) (9,12}
9. Which one of the following sets is a multiple of 3 in set. A ?

1) (6,9)

2) (6,11)

3) (9,12)

4) (6,9,12}

10. If A = {3, 4} , B = {2, 4} x ∈ A and y ∈ B , then determine the relation x > y ∈ A and B.
11. IfC = {2, 5} , D = {4, 6, 7} x ∈ C and y ∈ D then determine the relation x + 1 < y ∈ C and D.
12. If f(x) = x ^ 4 + 5x – 3 then determine f(- 1), f(2) and f(1/2)
13. If f(y) = y³ + k * y² – 4y – 8 then for what value of k will f(- 2) =0? 14. If f(x) = x³ – 6x² + 11x – 6 then for what value of r is f(x) =0?
14. If f(x) = (2x + 1)/(2x – 1) then determine the value of (f(1/(x²)) + 1)/(f(1/(x²)) – 1)
15. If g(x) = (1 + x² + x ^ 4)/(x²) prove that g(1/(x²)) = g(x²)
16. Determine domain and range from the following relations.

1) R = {(2, 1), (2, 2), (2, 3)}

2) S = {(- 2, 4), (- 1, 1), (0, 0), (1, 1), (2, 4)}

3) F = {(1/2, 0), (1, 1), (1, – 1), (5/2, 2), (5/2, – 2)\}

18. Express the following relations in tabular method and determine domain and range for each.

1) R={ (x,y):x ∈ A,y ∈ Aan * dx + y = 1} where A ={{- 2, – 1, 0, 1, 2\} 2) F={ (x,y):x ∈ C,y in Can * dy = 2x \ where C = \{- 1, 0, 1, 2, 3\}

19. Draw the points (-3,2), (0,-5), (1/2, – 5/6) on graph paper.
20. 20. Draw the points (1,2), (-1, 1), (11,7) on the graph paper and show that all the three points are on the same straight line.

21. Universal set U ={ x:x ∈ N and z odd number}, A={x:x ∈ N and * 2 <= x <= 7 }

B={x:x in N and * 3 < x < 6 }

C={x:x in N and * x² > 5and * x³ < 130 }

1) Express set A in tabular method.

2) Determine A’ and C \B

3) Determine BC and P( A ∩ C).

22. Look at the Venn diagram.

1) Express the set B building method.

2) Using the facts mentioned above, verify the relation A , ∪(B ∩C)=

( A ∪B) ∩(A ∪C). 

3) If S=(B ∪C)^c A then determinedom S.

23. y = f(x) = (4x – 7)/(2x – 4) is a function.

1) Determine the value of f(- 1/2)

2) Determine the value of (f(x) + 2)/(f(x) – 1)

3) Prove that f(y) = x

 

 

     24.Draw the graph for the function as belows.

1) y = 3x + 5

2) x + y = 2

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