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- 6.3. Let (A,⁸What is the correct aanswer(a) How many injective functions are there from {1, 2, 3} to {1, 2, 3, 4, 5, 6, 7}? (b) How many subsets are there of {1, 2, 3, 4, 5, 6, 7} that are the range of an injective function with domain {1, 2, 3}? (c) What is the smallest number of people that must be in a group in order to guarantee that at least three people in the group were born in the same month (of possibly different years)? (The answer is not three; if you have three people they could all be born in the same month, but this is not guaranteed). (d) What is the coefficient of a a^5b^2 in (a + b)^7? (e) What is the coefficient of a^5b^2c in (a + b + c)^8?2. Let S = {Canada, France, India, Japan, Norway, Philippines, USA} and II( S) = {{Canada, USA}, {France, Norway}, (India, Japan, Philippines}}. Determine the equiva- lence relation p rising from the partition. %3D 3. Let N = {1, 2, 3, ., 18, 19, 20}. Define the relation p on N20 as rpy iff zly. a. Show that (N- ) is a poset. b. Determine three chains that are contained in (N. 1).NoneShow the following set is convex. x10 Determine a-cut sets of the above set for a=0.5, 0.8 and 0.9.* If g € ([a,b] and g(x) € [a,b] for all x € [a, b] then g has only one fixed point in[a, b] true O false O4. Let X = {n €N : 10DISCRETE MATHEMATICSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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