Question

Find A∪B, A∩B, A–B and B–A for A = Set of all letters in the word "mathematics" and
B = Set of all letters in the word "geometry"

Answer 1

$\large\bf\underline{Given:-}$

• A = set of all letters in the word "MATHEMATICS"

• B = set of all letters in the word "GEOMETRY"

$\large\bf\underline {To \: find:-}$

• A∪B,
• A∩B,
• A–B
• B–A

$\huge\bf\underline{Solution:-}$

A = set of all letters in the word "MATHEMATICS"

• A = { M , A , T ,H , E, M, I, C, S}

B = Set of all letters in the word "GEOMETRY"

• B = {G , E, O ,M ,T, R ,Y}

NOW,

A∪B = {M , A ,T ,H ,E, I, C ,S, G , O , R, Y}

A∩B = {E, M ,T ,}

A–B = {A , H , I , C ,S}

B–A = {G , O , R ,Y }

$\rule{200}3$

Note:-

◑ A set can be written in any order.

Like:- we have a set A = {1 ,2 ,3 ,4 ,5, 6}

set A can also be written as :-

A = { 2 ,1 , 4, 3 ,5 ,6}

we can write any set in any order but the elements should not be changed and -

◑ Same element can not be repeated in sets.

like :- we have set A = {1 ,2 , 3, 3, 4 , 4 } = wrong. writing a set like this is wrong.

Correct form of this set A is :-

A = { 1, 2 , 3, 4}

there is only four elements in set A .

$\rule{200}3$

Answer 2

$\purple{\bf{\underline{We\:are\:given:-}}}$

▪A = Set of all letters in the word "mathematics".

▪B = Set of all letters in the word "geometry".

$\pink{\bf{\underline{We\:have\:to\:find:-}}}$

▪A ᑌ B

▪A ᑎ B

▪A - B

▪B - A

$\huge\orange{\bf{\underline{Solution:-}}}$

According to the question,

✮ A = { m, a, t, h, e, i, c, s}

✮ B = {g, e, o, m, t, r, y}

∴ A ᑌ B = {m, a, t, h, e, i, c, s, g, o, r, y}

∴ A ᑎ B = {m, e, t}

∴ A - B = {a, h, i, c, s}

∴ B - A = {g, o, r, y}

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$\green{\bf{\underline{Additional\:Informations:-}}}$

✦ The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. In symbols, . For example, if A = {1, 3, 5, 7} and B = {1, 2, 4, 6, 7} then A ∪ B = {1, 2, 3, 4, 5, 6, 7}.

✦ In mathematics, the intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B (or equivalently, all elements of B that also belong to A).

✦ A way of modifying a set by removing the elements belonging to another set. Subtraction of sets is indicated by either of the symbols – or \. For example, A minus B can be written either A – B or A \ B. See also. Intersection, union, Venn diagrams.

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