Reference no: EM132379446

Assignment -

Directions - Name your scripts 253-yourlastname-?-?.py. For example, my submission for P3 problem 4 would be a file 253-pauli-3-4.py.

(1) (PT) Read and work through the examples in

§3.1.3: Lists

§5.1.3: List Comprehensions

§5.4.: Sets

(2) (NP) Read and work through the examples in

• Lists

(3) Write a script that contains the following. For each part, first print the number to make it easier to grade.

(a) A function is_subset(A,B) that for two sets A and B returns True if A ⊆ B and False otherwise. Use a for loop and in but not the build-in <=.

(b) A function is_proper_subset(A,B) that for two sets A and B returns True if A ⊂ B and False otherwise. Use a for loop and in but not the build-in <.

(c) Verification whether your functions work correctly by using them to determine whether the following are true or false. Use set comprehensions to construct sets given in set builder notation.

(i) ∅ ⊂ ∅

(ii) ∅ ⊆ ∅

(iii) {1, 2, 3} ⊆ ∅

(iv) ∅ ⊆ {1, 2, 3}

(v) {1, 2, 3} ⊆ {1, 2, 3}

(vi) {1, 2, 3} ⊂ {1, 2, 3}

(vii) {1, 4} ⊆ {x²|x ∈ {1, 2, 3, . . . , 20}}

(viii) {4, 10} ⊆ {x| x ∈ {1, 2, 3, . . . , 50} Λ x mod 3 = 1}

(ix) {x²|x ∈ {1, 2, 3, . . . , 50} Λ x mod 3 = 0} ⊂ {3, 81}

(4) Write a script that contains the following. For each part, first print the number to make it easier to grade.

(a) A function cartesian_product(A, B) that returns the cartesian product of two sets A and B. You can represent the tuple (a, b) either as a tuple or a list with two elements.

(b) Verification whether your functions works correctly by using them to compute the following cartesian products:

(i) {1, 2, 3} x {5, 6}

(ii) {1, 2} x {2}

(iii) {7} x {1, 2, 3, 4}

(iv) ∅ x {1, 2, 3, 4}

(v) {1, 2, 3, . . . , 40} x {1, 2}

Attachment:- Assignment File.rar