a) Verify that,
(AnB) and (AuB) are equal for the following set A={1,3,4} B={2,3,4,5} U={1,2,3,4,5} (5 marks)
b) The weights (W) of female college students are linearly related to their heights (h)if a student of height 62 inches and weight of 120 pounds and a student of height 72 inches and weight of 170 pounds. Determine the equation that expresses their weight (w) in terms of height (h) of a student hence find the height of a student whose weight is 150 pounds. (5marks)
c) In a class of 80 students:
50 know English, 55 know French and 46 know German
37 know English and French
25know English and German
28 know French and German
7 know none of the language
Find,
i. How many students know all 3 languages? (3marks)
ii. How many students know exactly 2 languages(1 mark)
iii. How many students know exactly one language (1 mark)
iv. Represent the above information in a Venn diagram (4 marks)
d) Given a function f(x) =7-4x and g(x) =10-6x find value of:
3-5x 2-8x
i. Fog and state its domain. (4 marks)
ii. (fog)^-1 and state its domain.(3 marks)
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