Sets — Practice

Question 1

If A = {a, b, c}, write the power set P(A) and state its cardinality.

Accepted Answer

P(A) = {∅, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}}. Cardinality = 2³ = 8 elements.

Question 2

In a class of 60 students, 35 play cricket, 28 play football, and 15 play both. How many students play neither sport?

Accepted Answer

Step 1: n(C∪F) = n(C)+n(F)−n(C∩F) = 35+28−15 = 48. Step 2: Students playing at least one sport = 48. Step 3: Students playing neither = 60−48 = 12.

Question 3

If U = {1,2,3,4,5,6,7,8}, A = {1,3,5,7}, B = {2,3,4,5}, verify De Morgan's law: (A∪B)' = A'∩B'.

Accepted Answer

Step 1: A∪B = {1,2,3,4,5,7}. Step 2: (A∪B)' = U−(A∪B) = {6,8}. Step 3: A' = {2,4,6,8}, B' = {1,6,7,8}. Step 4: A'∩B' = {6,8}. Since (A∪B)' = A'∩B' = {6,8}, De Morgan's law is verified.

Practice — Sets

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