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Fundamental Theorem of Arithmetic

A=x: x is the...

Question

A={x:x is the factor of 24,x belongs to N}

B={x:x is the prime number,x<30}

Then find AUB, A intersection B, A-B, B-A.

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Solution

Given A={x:x is factor of 24}
we will find all the factors of 24 and include them in set A
∴A={1,2,3,4,6,8,12,24}
similarly for set B
B={2,3,5,7,11,13,17,19,23,29}
A∪B={1,2,3,4,5,6,7,8,11,12,13,17,19,23,24,29} is elements of A or B
A∩B={2,3} is common elements between the sets A and B
A-B= {1,4,6,8,12,24} is the set of elements of A which are not in B.
Similar way, B-A={5,7,11,13,17,19,23,29} is the set of elements of B which are not in A.

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Similar questions

Q. Find the cardinal number of the following sets.
(i)

A =

x : x

is a prime factor of 12 }
(ii)

B = {x : x \in W, x \leq 5}

If $A = {x : x i s a p r i m e n u m b e r}$ and

$B = {x : x \leq 10, x \in N}$

Then A ∩ B is

A \cup B

A \cap B

for the following sets.
(i)

A = {0, 1, 2, 4, 6}

B = {- 3, - 1, 0, 2, 4, 5}

A = {2, 4, 6, 8}

B = \emptyset

A = {x : x \in N, x \leq 5}

B =

x : x

is a prime number less than 11}
(iv)

A = {x : x \in N, 2 < x \leq 7}

B = {x : x \in W, 0 \leq x \leq 6}

Q. Find the intersection of each pair of sets:
(i) X={

1, 3, 5

1, 2, 3

a, e, i, o, u

a, b, c

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3

x : x

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B = ϕ

If $A = {x : x is a prime number}$ and

$B = {x : x \leq 10, x \in N},$ then $A \cap B$ = ___.

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