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Solution Code: 1IIG

Question:Maths

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Maths Assignment

Assignment Task

1 . Let us have the following sets A = {u,v,w} B = {{u},{v},{w}} C = {u, v, w,{v},{u,v,w}} D = {{w},{v},{u},{u,v,w}}. Discuss the validity of the following statements (explain why some are true and why the others are not true). (a) A = B (d) A ? C(g) B ? D (b) A ? B(e) A ? D(h) B ? D (c) A ? C(f) C ? D (i) A ? D 2 . Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric and/or transitive, where (a, b) ? R if and only if a) a runs faster than b; b) a and b graduated on the same day; c) a and b have a common cousin. 3 .Sets describing intervals of real numbers are expressed with brackets and endpoints: a square bracket [ ] if the endpoint is included, a round bracket ( ) if the endpoint is excluded. Let A = [2,6). Then A is the set of all real numbers from 2 to 6, including 2 but not including 6. Also let us have the sets B = (1,4) and C = [0,2]. (a) Write as intervals the 3 possible pairwise intersections and the 3 possible unions of sets A,B,C. Name the resulting sets as D, E, ... (b) You have 9 sets now. Define a relation ? to be “is a subset of” ?, on the set consisting of all 9 intervals you get. Write down the ordered pairs of this relation and draw the Hasse diagram of this partial ordering. 4 . Define the relation ? on the set S = {a, b, c, d, e, f} by ? = {(a, a),(b, b),(c, c),(d, d),(e, e),(f,f)(a, b),(b, a),(a, c),(c, a), (b, c),(c, b),(d, e),(e, d),(d, f),(f,d),(e, f),(f,e)} (a) Draw the directed graph of this relation. (b) Verify that this is an equivalence relation. Write down its equivalence classes. 5 . Given the binary relations on the set A = {1,2,3,4} defined by: ?1 = {(1,2),(1,3),(2,2),(2,3),(4,4)} and ?2 = {(2,4),(3,1),(3,2),(3,3),(4,3)} determine (construct the ordered pairs) of the composite relations: a) ?21 (b) ?1 ? ?2 (c) ?2 ? ?1 (d) ?1 ? ?2 ? ?1 properties of determinants
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    Maths Maths Maths
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