Applied Mathematics · Ch 3 — Sets

Operations on Sets

3.10

Operations on Sets

Sets are the building blocks of mathematics, and just as we add or multiply numbers, we can combine and compare sets using special operations. These operations—union, intersection, difference, and complement—let us create new sets from existing ones, revealing relationships and structures that are not obvious at first glance. Understanding them is essential for everything from probability to logic, and they form the language in which much of higher mathematics is written. …

Figure 3.3A Venn diagram of the union A ∪ B: both circles are shaded, representing all elements in A or B or both

Fig. 3.3 — A Venn diagram of the union A ∪ B: both circles are shaded, representing all elements in A or B or both

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

A ∪ B (shaded) is everything in A, in B, or …

Figure 3.4A Venn diagram of the intersection A ∩ B: only the overlapping lens region is shaded, the elements common to both sets

Fig. 3.4 — A Venn diagram of the intersection A ∩ B: only the overlapping lens region is shaded, the elements common to both sets

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

A ∩ B (shaded) is the overlap — the elements common to …

Figure 3.5A Venn diagram of the difference A − B: the part of A outside B is shaded, the elements in A but not in B

Fig. 3.5 — A Venn diagram of the difference A − B: the part of A outside B is shaded, the elements in A but not in B

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

A − B (shaded) is the part of A that lies ou …

Figure 3.6A Venn diagram of the complement A prime: everything in the universal set U outside A is shaded

Fig. 3.6 — A Venn diagram of the complement A prime: everything in the universal set U outside A is shaded

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

A' (shaded) is everything in the universal set U that is …

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← Previous · 3.9Example 13 — Let U = \1, 2, 3, 4, 5\, A = \1, 2, 3\ and B = \1, 2\. Represent the r…Next · 3.10 →Q1 — For the following sets, find their union and intersection. (i) A = \x …