Q. 165.0( 1 Vote )

# Write down the power sets of the following sets.

i. A = {x, y}

ii. X = {a, b, c}

iii. A = {5, 6, 7, 8}

iv. A = Φ

Answer :

Power set is nothing but all the possible combinations of the available set. Which can form a subset of that power set. For a set with ‘n’ elements, we will have 2^{n} elements in the power set.

i. P(A) = {Φ {x}, {y}, {x, y}} - 2^{2} =4 elements

ii. P(X)= {Φ, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}} – 2^{3} =8 elements

iii. P(A) = {Φ, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8}, {5, 6, 7, 8}} – 2^{4} =16 elements

iv. P(A) = {Φ} – 2^{0} =1=one element

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a)

b)

c)

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