Power Set of a Set!

Algebra Level 2

Let A, B and C be 3 sets defined as follows:

A = { 1, 2, 3, a, b}

B = { 1, 4, 6, a, c} and

C = { 1, 4, 8, a, d} .

Let M be the set so that M = (A\B)∩C .

If n is the number of element(s) in P(M) , the Power Set of M , then what is the value of ?


The answer is 2.

Muhammad Rasel Parvej by Muhammad Rasel Parvej , 27, Bangladesh

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1 solution

Munem Shahriar
Jan 23, 2018

M = ( A \ B ) ∩ C = { 1 , 2 , 3 , a , b } \ { 1 , 4 , 8 , a , d } ∩ C = { 2 , 3 } ∩ { 1 , 4 , 8 , a , d } = { } \begin{aligned} M &= (A \backslash B) \cap C \\ & = \{1,2,3,a,b\} \backslash \{1,4,8,a,d\} \cap C \\ & = \{2,3\} \cap \{1,4,8,a,d\} \\ &= \{ ~ \} \\ \end{aligned}

Hence the number of elements in P ( M ) P(M) is 2 n = 2 1 = 2 2^n = 2^1 = \boxed{2}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Munem!

In second line there is a typo.

M = { 1 , 2 , 3 , a , b } \ { 1 , 4 , 8 a , d } ∩ C M = \{1,2,3,a,b\} \backslash \{1,4,8 a,d\} \cap C

It must be

M = { 1 , 2 , 3 , a , b } \ { 1 , 4 , 8 , a , d } ∩ C M = \{1,2,3,a,b\} \backslash \{1,4,8,a,d\} \cap C

Harison Allan - 3 years, 4 months ago

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Thanks. I fixed it.

Munem Shahriar - 3 years, 4 months ago

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