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Set Theory

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Mathematics

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Homework

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qrkqrk07

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Set theory

1. Regions representing (A B) C

{II, IV, V, VI, VII}

Region representing (A B) C

{I, II, III, IV, V, VI}

2. Cardinal numbers in the given sets

C = {x I x is letter in the word six}

C = {SIX}

n(C) = 3

B = {x I x < 4 and x ≥ 12}

B = {4 > X ≥ 12}

n(B) = ∞

3. Number of subsets

• {2,4,6,8,10,12}

Number of subsets = 2

n

where n is number of elements

n = 6

2

6

= 64

Number of proper subsets = 2

n

-1, where n is number of elements

n = 6

= 2

6

-1

= 63

• {x I x is a day of the week}

{M, T, W, TH, F, SA, SU}

n = 7

Number of subsets = 2

n

where n is number of elements

n = 7

2

7

= 128

Number of proper subsets = 2

n

-1, where n is number of elements

n = 7

= 2

7

-1

= 127

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Set theory 1. Regions representing (A B) C {II, IV, V, VI, VII} Region representing (A B) C {I, II, III, IV, V, VI} 2. Cardinal numbers in the given sets C = {x I x is letter in the word six} C = {SIX} n(C) = 3 B = {x I x < 4 and x ≥ 12} B = {4 > X ≥ 12} n(B) = ∞ 3. Number of subsets • {2,4,6,8,10,12} Number of subsets = 2n where n is number of elements n=6 26 = 64 Number of proper subsets = 2n-1, where n is number of elements n=6 = 26-1 = 63 • {x I x is a day of the week} {M, T, W, TH, F, SA, SU} n=7 Number of subsets = 2n where n is number of elements n=7 27 = 128 Number of proper ...
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