A set problem

Probability Level 2

U = { x : x, positive number and x < 9 } U = \{ \text{x : x, positive number and x < 9} \}

M = { 2 , 5 , 6 } M = \{2,5,6\}

P = { 3 , 4 , 5 } P = \{3,4,5\}

R = { x : x, positive even number and x ≤ 6 } . R = \{ \text{x : x, positive even number and x ≤ 6} \}.

What is ( R ∪ P ) ∩ ( M − P ) ? (R \cup P) \cap (M - P)?

{ 2 , 3 , 4 , 5 , 6 } \{2,3,4,5,6\} { 2 , 3 } \{2,3\} { 2 , 6 } \{2,6\} { 2 , 3 , 4 } \{2,3,4\} { 2 , 4 } \{2,4\} { 2 , 4 , 6 , 8 } \{2,4,6,8\}

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Aug 20, 2017

Given that,

  • M = { 2 , 5 , 6 } M = \{2,5,6\}

  • P = { 3 , 4 , 5 } P = \{3,4,5\}

U = { x : x, positive number and x < 9 } U = \{ \text{x : x, positive number and x < 9} \}

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

R = { x : x, even number and x ≤ 6 } . R = \{ \text{x : x, even number and x ≤ 6} \}.

= { 2 , 4 , 6 } = \{2,4,6\}

Now,

( R ∪ P ) ∩ ( M − P ) (R \cup P) \cap (M - P)

= { 2 , 4 , 6 } ∪ { 3 , 4 , 5 } ∩ ( M − P ) = \{2,4,6\} \cup \{3,4,5\} \cap (M - P)

= { 2 , 3 , 4 , 5 , 6 } ∩ { 2 , 5 , 6 } − { 3 , 4 , 5 } = \{2,3,4,5,6\} \cap \{2,5,6\} - \{3,4,5\}

= { 2 , 3 , 4 , 5 , 6 } ∩ { 2 , 6 } =\{2,3,4,5,6\} \cap \{2,6\}

= { 2 , 6 } = \{2,6\}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it the exact same way, but I used Venn diagrams to evaluate some of the expressions. For me, that's an easier way to Evaluate expressions like ( R ∪ P (R \cup P ) and ( M − P (M - P ) rather than just doing all in my head.

Deva Craig - 3 years, 9 months ago

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