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Maths 1 week 1 important questions

Week 1 of Mathematics for Data Science I: Sets, relations, functions. Extra important questions based on the recent, changing patterns of the exams, from basic to advanced. Practise them in learning mode: each question has a worked solution.

Question 1

One or more correct options

Let A={1, 2, {3,4}}A = \{1,\ 2,\ \{3,4\}\}. Select all the true statements.

Select all that apply.

  1. A

    ∣A∣=3|A| = 3

  2. B

    {3,4}⊆A\{3,4\} \subseteq A

  3. C

    {1,2}⊆A\{1,2\} \subseteq A

  4. D

    {3,4}∈A\{3,4\} \in A

  5. E

    3∈A3 \in A

Question 2

Numerical answer

Let B={n∈Z+:n is odd and n2<150}B = \{n \in \mathbb{Z}^+ : n \text{ is odd and } n^2 < 150\}. How many elements does BB have?

Question 3

One or more correct options

Consider P={x∈Z:x2=4}P=\{x\in\mathbb{Z}: x^2=4\}, Q={x∈Z:∣x∣=2}Q=\{x\in\mathbb{Z}: |x|=2\}, R={x∈Z:x3−4x=0}R=\{x\in\mathbb{Z}: x^3-4x=0\} and T={2}T=\{2\}. Select all the true statements.

Select all that apply.

  1. A

    P=QP = Q

  2. B

    ∣R∣=2|R| = 2

  3. C

    R=PR = P

  4. D

    Q⊆RQ \subseteq R

  5. E

    T⊂PT \subset P (proper subset)

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