ma3001_2026T2_Q1_NA.pdf

Discrete Mathematics · Quiz 1 · May 2026

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Question 2 MSQ · 2.0 marks

Choose the set/s containing [[IMAGE:8ccbfe9625008eab_2_2]] as an element.

[[IMAGE:8ccbfe9625008eab_2_3]]
[[IMAGE:8ccbfe9625008eab_2_4]]
[[IMAGE:8ccbfe9625008eab_2_5]]
[[IMAGE:8ccbfe9625008eab_2_6]]
[[IMAGE:8ccbfe9625008eab_2_7]]

A published solution is not available for this question yet.

Question 3 MSQ · 2.0 marks

Which of the following statements is/are correct?

[[IMAGE:8ccbfe9625008eab_2_8]]
[[IMAGE:8ccbfe9625008eab_2_9]]
[[IMAGE:8ccbfe9625008eab_3_10]]
[[IMAGE:8ccbfe9625008eab_3_11]]
[[IMAGE:8ccbfe9625008eab_3_12]]

A published solution is not available for this question yet.

Question 4 MSQ · 4.0 marks

Which of the statements is/are correct?

[[IMAGE:8ccbfe9625008eab_3_13]]
[[IMAGE:8ccbfe9625008eab_3_14]]
[[IMAGE:8ccbfe9625008eab_3_15]]
[[IMAGE:8ccbfe9625008eab_3_16]]

A published solution is not available for this question yet.

Question 5 MSQ · 4.0 marks

Consider the following statement: If [[IMAGE:8ccbfe9625008eab_3_17]] is true, then [[IMAGE:8ccbfe9625008eab_3_18]] is true. We prove the above statement using the following sequence of arguments. 1. [[IMAGE:8ccbfe9625008eab_3_19]] 2. [[IMAGE:8ccbfe9625008eab_3_20]] 3. [[IMAGE:8ccbfe9625008eab_3_21]] 4. [[IMAGE:8ccbfe9625008eab_3_22]] 5. [[IMAGE:8ccbfe9625008eab_4_23]] 6. [[IMAGE:8ccbfe9625008eab_4_24]] 7. [[IMAGE:8ccbfe9625008eab_4_25]] Which statement/s of the above argument is/are erroneous?

Step 3
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Step 6
Step 7

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Question 6 NAT · 3.0 marks

Sometimes the number of times that an element occurs in an unordered collection matters. **Multisets** are unordered collections of elements where an element can occur as a member more than once. The notation [[IMAGE:8ccbfe9625008eab_4_26]] denotes the multiset with element [[IMAGE:8ccbfe9625008eab_4_27]] occurring [[IMAGE:8ccbfe9625008eab_4_28]] times, element [[IMAGE:8ccbfe9625008eab_4_29]] occurring [[IMAGE:8ccbfe9625008eab_4_30]] times, and so on. The numbers [[IMAGE:8ccbfe9625008eab_4_31]] are called the multiplicities of [[IMAGE:8ccbfe9625008eab_4_32]] . Let [[IMAGE:8ccbfe9625008eab_4_33]] and [[IMAGE:8ccbfe9625008eab_4_34]] be multisets. The union of the multisets [[IMAGE:8ccbfe9625008eab_4_35]] and [[IMAGE:8ccbfe9625008eab_4_36]] , denoted as [[IMAGE:8ccbfe9625008eab_4_37]] , is the multiset where the multiplicity of an element is the maximum of its multiplicities in [[IMAGE:8ccbfe9625008eab_4_38]] and [[IMAGE:8ccbfe9625008eab_4_39]] . Similarly, the intersection of the multisets [[IMAGE:8ccbfe9625008eab_4_40]] and [[IMAGE:8ccbfe9625008eab_4_41]] , denoted as [[IMAGE:8ccbfe9625008eab_4_42]] , is the multiset where the multiplicity of an element is the minimum of its multiplicities in [[IMAGE:8ccbfe9625008eab_4_43]] and [[IMAGE:8ccbfe9625008eab_4_44]] . Consider the multisets [[IMAGE:8ccbfe9625008eab_4_45]] and [[IMAGE:8ccbfe9625008eab_4_46]] . Answer the given subquestions with respect to the same.

What is the multiplicity of [[IMAGE:8ccbfe9625008eab_5_47]] in [[IMAGE:8ccbfe9625008eab_5_48]] ?

A published solution is not available for this question yet.

Question 7 NAT · 3.0 marks

What is the multiplicity of [[IMAGE:8ccbfe9625008eab_5_49]] in [[IMAGE:8ccbfe9625008eab_5_50]] ?

A published solution is not available for this question yet.

Question 8 NAT · 2.0 marks

Let [[IMAGE:8ccbfe9625008eab_5_51]] be the statement [[IMAGE:8ccbfe9625008eab_5_52]] , where [[IMAGE:8ccbfe9625008eab_5_53]] is the set of all non-negative integers. Consider the following inductive proof to prove [[IMAGE:8ccbfe9625008eab_5_54]] . Proof: Basis: _________________ Inductive step: Let [[IMAGE:8ccbfe9625008eab_5_55]] is true. Then [[IMAGE:8ccbfe9625008eab_5_56]] . So, [[IMAGE:8ccbfe9625008eab_5_57]] = (I) _____________= (II) _____________= [[IMAGE:8ccbfe9625008eab_5_58]] = [[IMAGE:8ccbfe9625008eab_6_59]] Answer the given subquestions with respect to the same.

What value of [[IMAGE:8ccbfe9625008eab_6_60]] should be used to prove the Basis?

A published solution is not available for this question yet.

Question 9 MCQ · 4.0 marks

Which of the following options correctly represent the statements that can be filled at (I) and (II) so that the proof will be correct?

(I) [[IMAGE:8ccbfe9625008eab_6_61]] , (II) [[IMAGE:8ccbfe9625008eab_6_62]]
(I) [[IMAGE:8ccbfe9625008eab_6_63]] , (II) [[IMAGE:8ccbfe9625008eab_6_64]]
(I) [[IMAGE:8ccbfe9625008eab_6_65]] , (II) [[IMAGE:8ccbfe9625008eab_6_66]]
(I) [[IMAGE:8ccbfe9625008eab_6_67]] , (II) [[IMAGE:8ccbfe9625008eab_6_68]]

A published solution is not available for this question yet.

Question 10 MCQ · 2.0 marks

Consider the following proposition and answer the given subquestions based on this proposition. [[IMAGE:8ccbfe9625008eab_7_69]]

Which of the following propositions is logically equivalent to the given proposition?

[[IMAGE:8ccbfe9625008eab_7_70]]
[[IMAGE:8ccbfe9625008eab_7_71]]
[[IMAGE:8ccbfe9625008eab_7_72]]
[[IMAGE:8ccbfe9625008eab_7_73]]

A published solution is not available for this question yet.

Question 11 MCQ · 2.0 marks

Consider the following proposition and answer the given subquestions based on this proposition. [[IMAGE:8ccbfe9625008eab_7_69]]

Which of the following propositions is a conjunctive normal form (CNF) of the given proposition?

[[IMAGE:8ccbfe9625008eab_7_74]]
[[IMAGE:8ccbfe9625008eab_7_75]]
[[IMAGE:8ccbfe9625008eab_7_76]]

A published solution is not available for this question yet.

Question 12 MCQ · 2.0 marks

Consider the following proposition and answer the given subquestions based on this proposition. [[IMAGE:8ccbfe9625008eab_7_69]]

Which of the following propositions is a disjunctive normal form (DNF) of the given proposition?

[[IMAGE:8ccbfe9625008eab_8_77]]
[[IMAGE:8ccbfe9625008eab_8_78]]
[[IMAGE:8ccbfe9625008eab_8_79]]

A published solution is not available for this question yet.

Question 13 MSQ · 3.0 marks

Let [[IMAGE:8ccbfe9625008eab_8_80]] and [[IMAGE:8ccbfe9625008eab_8_81]] , where [[IMAGE:8ccbfe9625008eab_8_82]] and [[IMAGE:8ccbfe9625008eab_8_83]] are constants. Determine under which of the following conditions it is true that [[IMAGE:8ccbfe9625008eab_8_84]] .

[[IMAGE:8ccbfe9625008eab_8_85]]
[[IMAGE:8ccbfe9625008eab_8_86]] and [[IMAGE:8ccbfe9625008eab_8_87]]
[[IMAGE:8ccbfe9625008eab_8_88]]
[[IMAGE:8ccbfe9625008eab_8_89]] or [[IMAGE:8ccbfe9625008eab_8_90]]
None of these

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Question 14 MSQ · 3.0 marks

Which of the following statements is/are true?

Every infinite set is uncountable
Union of two countable sets is countable
Intersection of two countable sets is countable
Set difference of two countable sets is countable

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Question 15 MCQ · 3.0 marks

Which of the following steps is wrong with this famous supposed "proof" that [[IMAGE:8ccbfe9625008eab_9_91]] ? Proof: We use the following steps, where [[IMAGE:8ccbfe9625008eab_9_92]] and [[IMAGE:8ccbfe9625008eab_9_93]] are two equal positive integers. 1. [[IMAGE:8ccbfe9625008eab_9_94]] 2. [[IMAGE:8ccbfe9625008eab_9_95]] 3. [[IMAGE:8ccbfe9625008eab_9_96]] 4. [[IMAGE:8ccbfe9625008eab_9_97]] 5. [[IMAGE:8ccbfe9625008eab_9_98]] 6. [[IMAGE:8ccbfe9625008eab_9_99]] 7. [[IMAGE:8ccbfe9625008eab_9_100]]

Step 3
Step 4
Step 5
Step 6
Step 7

A published solution is not available for this question yet.

Question 16 NAT · 4.0 marks

Fill in the blank: [[IMAGE:8ccbfe9625008eab_10_101]] ________ Enter the value as a single integer.

A published solution is not available for this question yet.

Question 17 MCQ · 2.0 marks

Consider the two sets: [[IMAGE:8ccbfe9625008eab_10_102]] the set of all negative integers that are multiples of [[IMAGE:8ccbfe9625008eab_10_103]] and [[IMAGE:8ccbfe9625008eab_10_104]] the set of all real numbers between [[IMAGE:8ccbfe9625008eab_10_105]] and [[IMAGE:8ccbfe9625008eab_10_106]] . Determine which of these sets are countable.

Both [[IMAGE:8ccbfe9625008eab_10_107]] and [[IMAGE:8ccbfe9625008eab_10_108]] are countable
[[IMAGE:8ccbfe9625008eab_10_109]] is countable but [[IMAGE:8ccbfe9625008eab_10_110]] is uncountable
[[IMAGE:8ccbfe9625008eab_10_111]] is countable but [[IMAGE:8ccbfe9625008eab_10_112]] is uncountable
Both [[IMAGE:8ccbfe9625008eab_10_113]] and [[IMAGE:8ccbfe9625008eab_10_114]] are uncountable

A published solution is not available for this question yet.

Question 18 NAT · 3.0 marks

Suppose [[IMAGE:8ccbfe9625008eab_11_115]] is a function defined recursively by: [[IMAGE:8ccbfe9625008eab_11_116]] [[IMAGE:8ccbfe9625008eab_11_117]] Answer the given subquestions with respect to the same.

Calculate [[IMAGE:8ccbfe9625008eab_11_118]] . Enter the value as a single integer.

A published solution is not available for this question yet.

Question 19 NAT · 2.0 marks

Calculate [[IMAGE:8ccbfe9625008eab_11_119]] . Enter the value as a single integer.

A published solution is not available for this question yet.