How many X subsets of {0, 1, 2,. . . , 9} if 0 ∈ X, 1 ∈ X and 2 ∈ / X?
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
How many subsets are there of 5 letters? How many contain at least one letter, but not all of the letters {a, b, c, d, e}?
How many ordered pairs (A, B), where A, B are subsets of {1 , 2, 3, 4, 5} have: |A ∩ B| = 1Where A ∩ B= {1} => 3^4 = 81
Calculate the number of subsets and the number of proper subsets for the set. 9) 9) 1, 3,5,7,9,11) A) 63; 62 B) 64; 63 C) 63; 64 D) 62; 63
Consider the following subsets of R2: C1 ={(x,y)∈R2 :x+y≤3,x≥0,y≥0} C2 ={(x,y)∈R2 :4x+y≤4,x≥0,y≥0} Algebra Consider the following subsets of R2. Draw a sketch of the intersection CinC2 and the union C1UC2. State whether each set is convex or not. If the set is not convex, give an example of a line segment for which the definition of convexity breaks down Algebra Consider the following subsets of R2. Draw a sketch of the intersection CinC2 and the union C1UC2. State whether each...
How Question:solve the system X 1 1 8 1 0 1 5 9 1 2 X 3
41. How many subsets does the set {a, b, c, d, e,f} have?
Algebra Consider the following subsets of R2: C1 = {(2, ) ER: x + 2y < 4, x > 0,y 0} C2 = {(x,y) € R2 : 2x + y < 4, x > 0, y 20} Draw a sketch of the intersection CinC, and the union CUC2. State whether each set is convex or not. If the set is not convex, give an example of a line segment for which the definition of convexity breaks down.
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them 2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
Show your work, please 5. Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of 2" in (3 - 2.c)"+3 (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?