What kind of set?

Probability Level 2

U = x : x, Positive numbers and 0 < x < 10 \text{U = {x : x, Positive numbers and 0 < x < 10 }}

A = x : x, Positive even numbers and 1 < x < 9 \text{A = {x : x, Positive even numbers and 1 < x < 9}}

B = { 1 , 2 , 4 , 6 , 8 } \text{B} = \{1, 2,4,6,8\}

Fill in the blank:

( A ∩ B ) ′ (A \cap B)' is a set of _______ \text{\_\_\_\_\_\_\_}

None of these Odd numbers Perfect numbers Even numbers Prime numbers

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Nov 23, 2017

( A ∩ B ) ′ (A \cap B)'

= U − ( A ∩ B ) = \text{U} - (A \cap B)

= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } − { 2 , 4 , 6 , 8 } ∩ { 1 , 2 , 4 , 6 , 8 } = \{1,2,3,4,5,6,7,8,9\} - \{2,4,6,8\} \cap \{1,2,4,6,8\}

= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } − { 2 , 4 , 6 , 8 } = \{1,2,3,4,5,6,7,8,9\} - \{2,4,6,8\}

= { 1 , 3 , 5 , 7 , 9 } = \{1,3,5,7,9\} is a set of odd numbers \boxed{\text{odd numbers}}

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