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Tutorial1(0211)

# Tutorial1(0211) - n B Find A ∪ B and A ∩ B 4 Let A =[0...

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T1/MATH0211/2009-10 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH0211 Basic Applicable Mathematics Tutorial 1 1. Let A = { α R : x 2 + αx + 4 = 0 has two distinct solutions } , B = { α R : x 2 + αx + 4 = 0 has exactly one solution } , C = { α R : x 2 + αx + 4 = 0 has no solutions } . (a) Express A and C in interval notation. (b) Represent B by the listing method. 2. Let S 1 = { ( x, 0) R 2 : 0 x 1 } , S 2 = { (1 , y ) R 2 : 0 y 1 } , S 3 = { ( x, 1) R 2 : 0 x 1 } , S 4 = { (0 , y ) R 2 : 0 y 1 } . (a) What is the geometric figure the set S 1 S 2 S 3 S 4 represents? (b) Use a similar method, represent the boundary of the right-angled triangle with vertices (0 , 0) , (3 , 0) and (3 , 2) . 3. Let A = { 1 , 3 , 5 , 7 } and B = {{ 1 , 3 } , { 5 } , 7 } . (a) List out all possible subsets of A that contains the element 1 . (b) List out all possible subsets of A that does not contain the element 3 . (c) What is

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Unformatted text preview: n ( B ) ? Find A ∪ B and A ∩ B . 4. Let A = [0 , 4] and B = (2 , 6] . Find (a) A ∪ B (b) A ∩ B (c) R \ A (d) ( R \ A ) ∪ ( R \ B ) 5. How many diﬀerent letter arrangement can be formed using the letters O E M AGA when (a) the two A ’s occupying end places; (b) E being always in the second place? 1 Discussion I. Let R = { ( x,y ) ∈ R 2 : y = x 2 } , S = { ( x,y ) ∈ R 2 : y = x 4 } . (a) Represent R and S in the same coordinate plane R 2 . (b) Find R ∩ S . What is its cardinality? II. Can you apply the ﬁrst formula in Theorem 1.37 (Chapter 1) to show that the second formula is true? 2...
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