Sets, Relations and Functions Two Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. State whether the following sets are finite or infinite.
    {x \(\in \) N:x is an odd prime number}

  2. State whether the following sets are finite or infinite.
    {x \(\in \) Z:x is even and less than 10}

  3. Let A and B be two sets such that n(A)=3 and n(B)=2. If (x, 1) (y, 2) (z, 1) are in A\(\times\)B, find A and B, where x, y, z are distinct elements.

  4. Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
    Reflexive

  5. If U={x:1≤x≤10, x∈N}, A={1,3,5,7,9} and B={2,3,5,9,10} then find A'UB'.

  6. If A⊂B then find A⋂B and A\B (using venn diagram)

  7. On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is reflexive

  8. On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is symmetric

  9. Find the number of subsets of A if A = \(\{x :x = 4n + 1, 2 \le n \le 5, n \in N\}.\)

  10. If f and g are two functions from R to R defined by f (x) = 4x - 3, g(x) = x2 + 1, find fog and gof.

  11. On a set of natural numbers let R be the relation defined by aRb if a + 2b = 15. Write down the relation by listing all the pairs. Check whether it is reflexive, symmetric, transitive, equivalence.

  12. If  \(f(x)=\frac { x-1 }{ x+1 } \), then show that \(f\left( \frac { 1 }{ x } \right) =-f(x)\)

  13. If  f(x)=\(\frac { x-1 }{ x+1 } \), then show that, f\(\left( \frac { -1 }{ x } \right) =\frac { -1 }{ f(x) } \).

  14. If A = { 0, 1, 2, 3, 4, 5, 6, 7 } is a set. Then,

  15. Try to write the following intervals in symbolic form:
    (i) \(\{x:x\in R,-2\le x \le 0 \},\) 
    (ii) \(\{ x:x\in R, 0<x< 8 \},\)
    (iii) \(\{ x:x \in R, -8\le -2 \}\)
    (iv) \(\{x:x\in R, -5\le x \le 9 \}\)

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