How deeply does Modern C, Third Edition cover set union?

Explains the set interpretation of bits, computes a worked union, and distinguishes union from related bitwise operations.

Set union

As explained in Modern C, Third Edition

Set union is the operation producing a set containing every element that belongs to either operand set.

Set union produces a set containing every element belonging to either operand set. For bit sets, C's | operator performs this operation bit by bit. section 5.7.2

Combining two bit sets

Let A = 240 represent {4, 5, 6, 7}, and B = 287 represent {0, 1, 2, 3, 4, 8}. Then A | B = 511 represents {0, 1, 2, 3, 4, 5, 6, 7, 8}. The shared element 4 appears once. section 5.7.2

Table 5.6 Effects of bitwise operators

Bit op	Value	Hex	𝑏₁₅…𝑏₈ 𝑏₇…𝑏₀	Set op	Set
`V`	`65,535`	`0x``FFFF`	`0b``11111111’11111111`		{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
`A`	`240`	`0x``00F0`	`0b``00000000’11110000`		{4, 5, 6, 7}
`~A`	`65,295`	`0x``FF0F`	`0b``11111111’00001111`	\(V \setminus A\)	{0, 1, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15}
`-A`	`65,296`	`0x``FF10`	`0b``11111111’00010000`		{4, 8, 9, 10, 11, 12, 13, 14, 15}
`B`	`287`	`0x``011F`	`0b``00000001’00011111`		{0, 1, 2, 3, 4, 8}
`A\|B`	`511`	`0x``01FF`	`0b``00000001’11111111`	\(A \cup B\)	{0, 1, 2, 3, 4, 5, 6, 7, 8}
`A&B`	`16`	`0x``0010`	`0b``00000000’00010000`	\(A \cap B\)	4
`A^B`	`495`	`0x``01EF`	`0b``00000001’11101111`	\(A \Delta B\)	{0, 1, 2, 3, 5, 6, 7, 8}

Compare the binary values, hexadecimal forms, and set interpretations of union, intersection, complement, and symmetric difference. section 5.7.2

In C bit sets, union has these practical properties:

Treats each unsigned value as a subset of a fixed base set whose members correspond to set bits. section 5.7.2
Uses |= to update a bit set by adding the bits present in another operand. section 5.7.2
Supports flags: setting a power-of-two flag adds that member to the represented set. section 5.7.2

In union-find, Union merges the two partition sets containing selected elements; Find identifies the root representing a partition set. section 4.6

How Modern C, Third Edition covers it

liveBook manning.com

Read Modern C, Third Edition on liveBook Get the book at manning.com

Also explained in

liveBook manning.com

Geometry for ProgrammersA geometric union is a Boolean set operation containing every point belonging to at least one of two or more shapes.
liveBook manning.com

Julia as a Second Languageunion is a Julia function and set operation that returns the distinct elements occurring in any of its input collections.
liveBook manning.com

Secrets of the JavaScript Ninja, Second EditionA set operation that produces a set containing every element present in either operand set.

Compare how 4 books explain set union →

Related concepts

setproduces · A set is a collection of unique elements in which membership is determined by whether an element is present, not by duplicate occurrences.
set operationkind of · A set operation combines, compares, or transforms sets according to the membership of their elements.
boolean operationkind of · A Boolean operation combines or modifies geometric regions using set-like operations such as union, intersection, and difference.
set!uses · set! is a Clojure mutation construct that assigns a value to a mutable target such as a field or thread-local binding.

This explainer was generated by Manning's knowledge graph from the text of Modern C, Third Edition. The section links point to the parts of the book it draws on.