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#### Sets, Relations and Functions Two Marks Questions

11th Standard

Reg.No. :
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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) $\{x:x\in R, -5\le x \le 9 \}$