Let A = { 1, 2, 3 } How many tuples are in the Cartesian product...
Let A = { 1, 2, 3 }
How many tuples are in the Cartesian product AxA ?
Homework Answers
Answer: 9
Explanation: Number of tuples of a product of two sets can be calculated by the number of tuples in set1 * number of tuples in set2. Here set1 and set2 both has 3 tuples. Therefore AXB has 3*3 = 9 tuples.
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3}...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Using Haskell Write a tripleDistance function that takes two 3-tuples and finds the cartesian distance use...
Using Haskell
Write a tripleDistance function that takes two 3-tuples and
finds the cartesian distance
use Haskell's sqrt, ^,
+, *, - as needed
Problem 1.4 (a) Let 2 = 3e32"/3. Convert z to Cartesian form. (b) Let z =...
Problem 1.4 (a) Let 2 = 3e32"/3. Convert z to Cartesian form. (b) Let z = 6 - 23. Convert z to polar form. (c) Let 2 = 1-. Calculate 25. (d) Let z be a complex number and 23 = V3+j. Find all possible values of 2.
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on...
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.
1. Let A be 1 more than the product of the primes 3, 5, and 7....
1. Let A be 1 more than the product of the primes 3, 5, and 7. Factor A into a product of primes and check how many of 3, 5,7 are factors of A. 2. Make a list consisting of a few of your favorite primes and let B be 1 more than the product of these primes. Factor B into a product of primes and check how many of the primes on your list are factors of B.
Consider tables R and S below How many tuples are in the natural join of R...
Consider tables R and S below How many tuples are in the natural join of R and S ? B) 4 c) 5 OD) 6 E) 7
Let A = { 1, 2, 3, 4, 5 }. Give examples of a relation over...
Let A = { 1, 2, 3, 4, 5 }. Give examples of a relation over AxA that has exactly 5 elements that satisfy each of the following properties: Reflexive: Irreflexive: Symmetric: Antisymmetric: Transitive:
do 4,5,6 Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a)...
do 4,5,6
Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
9) Let R and S be commutative rings. Show that the cartesian product is a ring with addition and ...
just 10 thank you
9) Let R and S be commutative rings. Show that the cartesian product is a ring with addition and multiplication s') := (r , rrs-s' ) . 10) Let T be a commutative ring containing elements e, f, both 07-such that e+f=h,e=e,f2 = f , and e-f=0T . Show that the ideals R: T e and S T.f are rings but not subrings of T, and that the ring T is isomorphic to the ring R...
Defn: Let X and Y be sets. Their Cartesian product, X X Y , is the...
Defn: Let X and Y be sets. Their Cartesian product, X X Y , is the set containing all ordered pairs (x, y) with x € X and Y EY. If Y = X we write X X X = X?. 8) Show that X x 0 = 0 x X = 0 for every set X.
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Using Haskell
Write a tripleDistance function that takes two 3-tuples and
finds the cartesian distance
use Haskell's sqrt, ^,
+, *, - as needed
Problem 1.4 (a) Let 2 = 3e32"/3. Convert z to Cartesian form. (b) Let z = 6 - 23. Convert z to polar form. (c) Let 2 = 1-. Calculate 25. (d) Let z be a complex number and 23 = V3+j. Find all possible values of 2.
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.
Consider tables R and S below How many tuples are in the natural join of R and S ? B) 4 c) 5 OD) 6 E) 7
do 4,5,6
Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
just 10 thank you
9) Let R and S be commutative rings. Show that the cartesian product is a ring with addition and multiplication s') := (r , rrs-s' ) . 10) Let T be a commutative ring containing elements e, f, both 07-such that e+f=h,e=e,f2 = f , and e-f=0T . Show that the ideals R: T e and S T.f are rings but not subrings of T, and that the ring T is isomorphic to the ring R...
Defn: Let X and Y be sets. Their Cartesian product, X X Y , is the set containing all ordered pairs (x, y) with x € X and Y EY. If Y = X we write X X X = X?. 8) Show that X x 0 = 0 x X = 0 for every set X.
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