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Unformatted text preview: Chapter 1 Sample Space and Probability 1 Sets • S ∪ T = { x ; x ∈ S or x ∈ T } and S ∩ T = { x ; x ∈ S and x ∈ T } – If S = {♣ , ♦ , ♥} and T = {♦ , ♥ , ♠} then S ∪ T = {♣ , ♦ , ♥ , ♠} and S ∩ T = {♦ , ♥} . – Shade on separate graphs S ∩ T and S ∪ T . S T S T – Let S be the set of (strictly) positive even integers and T be the set of integers less than or equal to 9. Then S ∪ T = { . . . , 2 , 1 , . . . , 8 , 9 , 10 , 12 , 14 , 16 , . . . } and S ∩ T = { 2 , 4 , 6 , 8 } . – Let S be the set of polynomials of degree less than or equal to 2 and T be the set of differentiable functions f with f (0) = f (0) = 0. Describe S ∩ T . • S c = { x ; x 6∈ S } , ( S c ) c = S , S ∩ S c = ∅ and S ∪ S c = Ω – If Ω = {♣ , ♦ , ♥ , ♠} and S = {♦ , ♥} then S c = {♣ , ♠} . – Shade on separate graphs S c ∩ T c and ( S ∪ T ) c . 1 2 MTH2222 – Mathematics of Uncertainty S T S T What do you notice? – Within the set of positive integers, what is the complement of the set of even integers? • S \ T = { x ; x ∈ S and x 6∈ T } = S ∩ T c – Shade S \ T and T \ S . S T • S Δ T = ( S \ T ) ∪ ( T \ S ) – What is ( S Δ T ) ∪ ( S ∩ T )? • S ∪ ( T ∩ U ) = ( S ∪ T ) ∩ ( S ∪ U ) S T U S T U Chapter 1 3 and S ∩ ( T ∪ U ) = ( S ∩ T ) ∪ ( S ∩ U ) S T U S T U • ∞ [ n =1 S n = S 1 ∪ S 2 ∪...
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 Two '10
 KaizHamza
 Probability, Probability theory, total probability theorem

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