TOPIC: SETS, RELATION AND FUNCTION

ANSWER ONLY PLEASE ANSWER ALL

1. Let the Universal set U= {1,2,3,4......,10}. Let A = {1,4,7,10}, B = {1,2,3,4,5} and C = {2,4,6,8}. List the elements of each set and draw its corresponding Venn Diagram

- U'

-B

-BUBU

-B(CA)B(CA)

- ABC

2. 100 students were interviewed. 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects. Draw the Venn Diagram

a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG? d) How many students took exactly 2 of 3 subjects? e) How many students took any 2 of 3 subjects? f) How many students took any of the 3 subjects? g) How many students took none of the 3 subjects?

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1. Consider the following relations on A = {t,u,v,w}. Determine whether these relations are reflexive, symmetric, anti-symmetric and transitive.

1. R1 = {(t,t), (t,u), (u,t), (u,u), (v,w), (w,t), (w,w)}

2. R2 = {(t,t), (t,u), (u,t)}

3. R3 = {(t,t), (t,u), (t,w), (u,t), (u,u), (v,v), (w,t), (w,w)}

4. R4 = {(u,t), (v,t), (w,t), (w,u), (w,v)}

5. R5 = {(t,t), (t,u), (t,v), (t,w), (u,u), (u,v), (u,w), (v,v), (v,w), (w,w)}

2. Let R and S be a relations from set A to set B given that A ={2,4,6} and B = {t,u,v,w}. R = {(2,t), (2,u), (2.v), (4,t), (4,w), (6,u), (6,w)}. Find the following:

1. R 2. R 3. R - 1 4. R-1 6. (R