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

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Graph the function f(x)=x3 and $g(x)\sqrt[3]x$ on the same co-ordinate plane. Find fog and graph it on the plane as well. Explain your results.

2. Write the steps to obtain the graph of the function y=3(x-1)2+5 from the graph y=x2

3. By taking suitable sets A, B, C, verify the following results:
(A$\times$ B)$\cap$(B$\times$A) = (A$\cap$B) $\times$ (B$\cap$A)

4. By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C$\cap$ A) $\cup$ (C$\cap$B')

5. If A$\times$ A has 16 elements, S={(a,b)$\in$A$\times$A:a: <b} : (-1; 2) and (0; 1) are two elements of S, then find the remaining elements of S.

6. Show that the function f: N ⟶ N given by f(x) = 2x is one-one but not onto

7. Show that the function f: R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

8. Find the pairs of equal sets from the following sets. A = {0}, B = {x: x > 15 and x < 5}, C = {x: x - 5 = 0}, D = {x: x2 = 25}, E = {x: x is an integral positive root of the equation x2 - 2x - 15 = 0}.

9. If a ∈ N such that aN = {ax: x ∈ N}. Describe the set 3N ∩ 7N.

10. Let A and B be two sets. Using properties of sets prove that A ∩ B' = Φ ⇒ A ⊂ B.