For A = \2, 4, 6\ and B = \4, 6, 8\, state A B. [1 mark]

EnglandComputer ScienceSyllabus dot point

What mathematical tools (sets, logic and quantitative comparison) underpin computer science?

Mathematical skills for computer science: set theory and set operations, the comparison of binary, denary and hexadecimal magnitudes, simple logic propositions, and the use of these tools to reason about data and algorithms.

An OCR H446 answer on the mathematical skills underpinning computer science: set theory and set operations, comparing magnitudes across binary, denary and hexadecimal, simple logic propositions, and applying these tools to reason about data and algorithms.

Generated by Claude Opus 4.813 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

Computer science uses several mathematical tools. Set theory describes collections of distinct elements: the union ( $A \cup B$ ) is everything in either set, the intersection ( $A \cap B$ ) is the elements in both, the difference ( $A \setminus B$ ) is the elements in $A$ but not $B$ , and a subset is a set wholly contained in another. Sets underlie databases, type systems and search. Comparing magnitudes across number bases requires converting them to a common base (usually denary) before ordering, because the same value can look different in binary, denary and hexadecimal. Simple logic propositions use AND, OR and NOT to combine true/false statements and are evaluated like Boolean expressions. These tools let you reason precisely about data, conditions and the efficiency of algorithms.

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What this dot point is asking

OCR wants the mathematical skills that support the course: set theory and its operations, comparing magnitudes expressed in binary, denary and hexadecimal, and simple logic propositions, used to reason about data and algorithms. Expect a set-operations question and a "put these values in order" question across number bases.

The answer

Set theory and set operations

Comparing magnitudes across number bases

Logic propositions

Order values and apply a set operation

The valid usernames in system A are $\{102, 150, 160\}$ and in system B are $\{150, 160, 200\}$ . (1) Find the usernames common to both. (2) Put the values $\text{A0}_{16}$ , $96_{10}$ and $1010\,0001_2$ in ascending order.

step 1: Find the common usernames (intersection)

The intersection $A \cap B$ is the elements in both sets: $\{150, 160\}$ . These users exist on both systems.

step 2: Convert the mixed-base values to denary

$\text{A0}_{16} = 10 \times 16 + 0 = 160$ . $96_{10} = 96$ . $1010\,0001_2 = 128 + 32 + 1 = 161$ .

step 3: Order the denary values

$96 < 160 < 161$ , so ascending order is $96_{10}$ , then $\text{A0}_{16}$ , then $1010\,0001_2$ .

step 4: State the answers

(1) The common usernames are $\{150, 160\}$ . (2) Ascending order: $96$ , $\text{A0}$ (=160), $1010\,0001$ (=161). Converting to a common base was essential to compare the magnitudes correctly.

Examples in context

Database queries are set operations: a join's matching rows are an intersection, and combining result sets is a union. Type systems define the set of values a variable may hold. Comparing file sizes or addresses given in hex and denary needs base conversion first. Logical propositions are the conditions in every if-statement. OCR links these skills to number representation, to Boolean algebra and logic, and to reasoning about algorithm efficiency with Big-O.

Try this

Q1. For $A = \{2, 4, 6\}$ and $B = \{4, 6, 8\}$ , state $A \cap B$ . [1 mark]

Cue. $\{4, 6\}$ (the elements in both sets).

Q2. Put $\text{1F}_{16}$ and $30_{10}$ in ascending order, showing your reasoning. [2 marks]

Cue. $\text{1F}_{16} = 1 \times 16 + 15 = 31$ ; $30 < 31$ , so the order is $30_{10}$ then $\text{1F}_{16}$ .

Q3. State what the union of two sets contains. [1 mark]

Cue. All elements that are in either set (or both), each listed once.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20205 marksTwo sets are

A = \{1, 2, 3, 4\}

and

B = \{3, 4, 5, 6\}

. State the union, the intersection and the difference

A \setminus B

, and explain what the intersection represents.

Show worked answer →

Union (1 mark): $A \cup B = \{1, 2, 3, 4, 5, 6\}$ (all elements in either set, listed once).

Intersection (1 mark): $A \cap B = \{3, 4\}$ (elements in both sets).

Difference (1 mark): $A \setminus B = \{1, 2\}$ (elements in $A$ but not in $B$ ).

Meaning of intersection (up to 2): the intersection is the set of elements common to both sets, here the values that appear in both $A$ and $B$ . Markers reward the three correct sets and a correct description of intersection as the common elements. A common error is including duplicates in the union or confusing intersection with union.

OCR 20214 marksPlace the following values in ascending order, showing your reasoning: the binary number

1010\,0000

, the hexadecimal number

\text{A0}

, and the denary number

150

Show worked answer →

Convert to a common base (up to 3): $1010\,0000$ in binary $= 128 + 32 = 160$ . $\text{A0}$ in hex $= 10 \times 16 + 0 = 160$ . The denary value is $150$ .

Order (1 mark): $150 < 160 = 160$ , so ascending order is $150$ , then $1010\,0000$ and $\text{A0}$ (which are equal at $160$ ). Markers reward converting all three to denary and the correct ordering, noting that the binary and hex values are equal. A common error is comparing the raw digit strings without converting.

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Sources & how we know this

OCR AS and A Level Computer Science (H046, H446) specification — OCR (2015)